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1
Zhuang, Min, Jiahao Huang, and Chaohong Lee. "Entanglement-enhanced test proposal for local Lorentz-symmetry violation via spinor atoms." Quantum 6 (November 14, 2022): 859. http://dx.doi.org/10.22331/q-2022-11-14-859.
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Invariance under Lorentz transformations is fundamental to both the standard model and general relativity. Testing Lorentz-symmetry violation (LSV) via atomic systems attracts extensive interests in both theory and experiment. In several test proposals, the LSV violation effects are described as a local interaction and the corresponding test precision can asymptotically reach the Heisenberg limit via increasing quantum Fisher information (QFI), but the limited resolution of collective observables prevents the detection of large QFI. Here, we propose a multimode many-body quantum interferometry for testing the LSV parameter κ via an ensemble of spinor atoms. By employing an N-atom multimode GHZ state, the test precision can attain the Heisenberg limit Δκ∝1/(F2N) with the spin length F and the atom number N. We find a realistic observable (i.e. practical measurement process) to achieve the ultimate precision and analyze the LSV test via an experimentally accessible three-mode interferometry with Bose condensed spin-1 atoms for example. By selecting suitable input states and unitary recombination operation, the LSV parameter κ can be extracted via realizable population measurement. Especially, the measurement precision of the LSV parameter κ can beat the standard quantum limit and even approach the Heisenberg limit via spin mixing dynamics or driving through quantum phase transitions. Moreover, the scheme is robust against nonadiabatic effect and detection noise. Our test scheme may open up a feasible way for a drastic improvement of the LSV tests with atomic systems and provide an alternative application of multi-particle entangled states.
2
Sugino, Fumihiko, and Vladimir Korepin. "Rényi entropy of highly entangled spin chains." International Journal of Modern Physics B 32, no. 28 (November 7, 2018): 1850306. http://dx.doi.org/10.1142/s021797921850306x.
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Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an “area law” which means that the entanglement entropy is proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. In this paper, we first analytically compute the Rényi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Rényi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Rényi entropy is known as a function of its parameter. We find nonanalytic behavior of the Rényi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the Rényi entropy of Rokhsar–Kivelson states in two dimensions.
3
Biercuk, M. J., H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger. "High-fidelity quantum control using ion crystals in a Penning trap." Quantum Information and Computation 9, no. 11&12 (November 2009): 920–49. http://dx.doi.org/10.26421/qic9.11-12-2.
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We provide an introduction to the use of ion crystals in a Penning trap for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled, and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials. We discuss the use of two-dimensional $^{9}$Be$^{+}$ ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state electron spin flip transition, which we drive using microwaves. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations ($\tau_{\pi}\sim$200 $\mu$s). Randomized Benchmarking demonstrates an error per gate (a Pauli-randomized $\pi/2$ and $\pi$ pulse pair) of $8\pm1\times10^{-4}$. Ramsey interferometry and spin-locking measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of $T_{2}\sim$2 ms, and a limiting $T_{1\rho}\sim$688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the error-suppressing capabilities of dynamical decoupling pulse sequences, demonstrating an ability to extend qubit coherence and suppress phase errors. We conclude with a discussion of future avenues for experimental exploration, including the use of additional nuclear-spin-flip transitions for effective multiqubit protocols, and the potential for Coulomb crystals to form a useful testbed for studies of large-scale entanglement.
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Subrahmanyam, V. "Macroscopic multispecies entanglement near quantum phase transitions." Quantum Information and Computation 11, no. 1&2 (January 2011): 1–7. http://dx.doi.org/10.26421/qic11.1-2-1.
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Multi-Species entanglement, defined for a many-particle system as the entanglement between different species of particles, is shown to exist in the thermodynamic limit of the system size going to infinity. This macroscopic entanglement, as it can exhibit singular behavior, is capable of tracking quantum phase transitions. The entanglement between up and down spins has been analytically calculated for the one-dimensional Ising model in a transverse magnetic field. As the coupling strength is varied, the first derivative of the entanglement shows a jump discontinuity and the second derivative diverges near the quantum critical point.
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ERYIĞIT, RECEP, RESUL ERYIĞIT, and YIĞIT GÜNDÜÇ. "QUANTUM PHASE TRANSITIONS AND ENTANGLEMENT IN J1–J2 MODEL." International Journal of Modern Physics C 15, no. 08 (October 2004): 1095–103. http://dx.doi.org/10.1142/s0129183104006558.
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We study ground state pairwise entanglement within one-dimensional spin-1/2 antiferromagnetic J1–J2 model with competing interactions. Contrary to some claims we found that frustration does not increase entanglement. Concurrence of nearest and next nearest neighbors are found to show abrupt change at phase transition points. We also show that the concurrence can be used to classify the phase diagram of the model in anisotropy–frustration plane.
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Latorre, J. I., E. Rico, and G. Vidal. "Ground state entanglement in quantum spin chains." Quantum Information and Computation 4, no. 1 (January 2004): 48–92. http://dx.doi.org/10.26421/qic4.1-4.
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A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.
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Zhang, Zhao, Amr Ahmadain, and Israel Klich. "Novel quantum phase transition from bounded to extensive entanglement." Proceedings of the National Academy of Sciences 114, no. 20 (May 1, 2017): 5142–46. http://dx.doi.org/10.1073/pnas.1702029114.
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The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating “useful” entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises.
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Wang, Lihua, and Sung Gong Chung. "Entanglement perturbation theory for infinite quasi-1D quantum systems." International Journal of Modern Physics B 29, no. 07 (March 2, 2015): 1550042. http://dx.doi.org/10.1142/s0217979215500423.
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We develop entanglement perturbation theory (EPT) for infinite Quasi-1D quantum systems. The spin-1/2 Heisenberg chain with ferromagnetic nearest neighbor (NN) and antiferromagnetic next nearest neighbor (NNN) interactions with an easy-plane anisotropy is studied as a prototypical system. The obtained phase diagram is compared with a recent prediction [Phys. Rev. B 81, 094430 (2010)] that dimer and Néel orders appear alternately as the XXZ anisotropy Δ approaches the isotropic limit Δ = 1. The first and second transitions (across dimer, Néel and dimer phases) are detected with improved accuracy at Δ ≈ 0.722 and 0.930. The third transition (from dimer to Néel phases), previously predicted to be at Δ ≈ 0.98, is not detected at this Δ in our method, strongly indicating that the second Néel phase is absent.
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CLARK, J. W., A. MANDILARA, M. L. RISTIG, and K. E. KÜRTEN. "ENTANGLEMENT PROPERTIES OF QUANTUM MANY-BODY WAVE FUNCTIONS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4041–57. http://dx.doi.org/10.1142/s0217979209063249.
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The entanglement properties of correlated wave functions commonly employed in theories of strongly correlated many-body systems are studied. The variational treatment of the transverse Ising model within correlated-basis theory is reviewed, and existing calculations of the one- and two-body reduced density matrices are used to evaluate or estimate established measures of bipartite entanglement, including the Von Neumann entropy, the concurrence, and localizable entanglement, for square, cubic, and hypercubic lattice systems. The results discussed in relation to the findings of previous studies that explore the relationship of entanglement behaviors to quantum critical phenomena and quantum phase transitions. It is emphasized that Jastrow-correlated wave functions and their extensions contain multipartite entanglement to all orders.
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BOSE, INDRANI, and AMIT KUMAR PAL. "QUANTUM DISCORD, DECOHERENCE AND QUANTUM PHASE TRANSITION." International Journal of Modern Physics B 27, no. 01n03 (November 26, 2012): 1345042. http://dx.doi.org/10.1142/s0217979213450422.
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Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
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Pakarzadeh, Hassan, Zahra Norouzi, and Javad Vahedi. "Time evolution of entanglement in a four-qubit Heisenberg chain." Quantum Information and Computation 20, no. 9&10 (August 2020): 736–46. http://dx.doi.org/10.26421/qic20.9-10-2.
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The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.
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Rodríguez Ramírez, Karen. "The Use of Entanglement Entropy to Classify Quantum Phase Transitions in 1D Ultracold Spinor Bosons." Revista de Ciencias 21, no. 1 (April 4, 2018): 23. http://dx.doi.org/10.25100/rc.v21i1.6342.
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In this paper, we discuss a novel method based on a quantum-information-toolsuitable to identify and characterize quantum-phases and phase transitions in a broad set of lattice models relevant in condensed-matter systems. The method relies on theentanglement entropy which, for instance, can be calculated using the Matrix ProductState (MPS) algorithm, or any other method, for several system sizes to perform an appropriate scaling. Particularly, this advanced method has been applied for a finite 1D system of repulsively interacting spin-1 bosons and obtaining the universality class via the calculation of the central charge for the extemal field-induced phase transitionbetween the dimerized phase and the XY-nematic phase in the antiferromagnetic regime.Finally, we briefly discuss how this method has been recently used to identify topologicalphases.
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Malinovsky, V. S., and I. R. Sola. "Phase control for entanglement preparation in two-qubit systems." Quantum Information and Computation 5, no. 4&5 (July 2005): 364–79. http://dx.doi.org/10.26421/qic5.45-7.
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The theory of Quantum Control is starting to lay bridges with the field of Quantum Information and Quantum Computation. Using key ideas of laser control of the dynamics by means of phase manipulation and adiabatic passage, we review laser schemes that allow entanglement preparation in a two-qubit system. The schemes are based on sequences that use four time-delayed pulses, with or without concerted decay, in or off resonance with the intermediate levels of the qubit space. We show how to control the fidelity and phase of the entanglement, as well as the sensitivity of the preparation to the different pulse parameters. In general the schemes provide an improvement in robustness and in the finesse of the control to phase, with respect to previously proposed schemes based on sequences of $\pi$ pulses.
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Qin, Meng, Xin Zhang, and Zhong-Zhou Ren. "Renormalization of quantum deficit and monogamy relation in the Heisenberg XXZ model." Quantum Information and Computation 16, no. 9&10 (July 2016): 835–44. http://dx.doi.org/10.26421/qic16.9-10-6.
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In this study, the dynamical behavior of quantum deficit and monogamy relation in the Heisenberg XXZ model is investigated by implementing quantum renormalization group theory. The results demonstrate that the quantum deficit can be used to capture the quantum phase transitions point and show scaling behavior with the spin chain size increasing. It was also found that the critical exponent has no change when varying measure from entanglement to quantum correlation. The monogamy relation is influenced by the steps of quantum renormalization group and the ways of splitting the block states. Furthermore, the monogamy relation of generalized W state also is given by means of quantum deficit.
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Chakravarty, Sudip. "SCALING OF VON NEUMANN ENTROPY AT THE ANDERSON TRANSITION." International Journal of Modern Physics B 24, no. 12n13 (May 20, 2010): 1823–40. http://dx.doi.org/10.1142/s0217979210064629.
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Extensive body of work has shown that for the model of a non-interacting electron in a random potential there is a quantum critical point for dimensions greater than two — a metal–insulator transition. This model also plays an important role in the plateau-to-plateu transition in the integer quantum Hall effect, which is also correctly captured by a scaling theory. Yet, in neither of these cases the ground state energy shows any non-analyticity as a function of a suitable tuning parameter, typically considered to be a hallmark of a quantum phase transition, similar to the non-analyticity of the free energy in a classical phase transition. Here we show that von Neumann entropy (entanglement entropy) is non-analytic at these phase transitions and can track the fundamental changes in the internal correlations of the ground state wave function. In particular, it summarizes the spatially wildly fluctuating intensities of the wave function close to the criticality of the Anderson transition. It is likely that all quantum phase transitions can be similarly described.
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Xiong, H. N., J. Ma, W. F. Liu, and X. Wang. "Quantum Fisher information for superpositions of spin states." Quantum Information and Computation 10, no. 5&6 (May 2010): 498–508. http://dx.doi.org/10.26421/qic10.5-6-8.
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In terms of quantum Fisher information, a quantity $\chi^{2}$ was introduced by Pezz\'{e} and Smerzi, which is a multiparticle entanglement measure, and provides a necessary and sufficient condition for sub-shot-noise phase estimation sensitivity. We derive a general expression of $\chi ^{2}$ for arbitrary symmetric multiqubit states with nonzero mean spins. It is shown that the entangled symmetric states are useful for phase sensitivity beyond the shot-noise limit. Using the expression, we explicitly examine a series of superpositions of spin states. We find that the superpositions of Dicke states perform better than Dicke states themselves in phase esitmation. Although the spin coherent states themselves only have a shot-noise limit phase sensitivity, their superpositions may reach the Heisenberg limit.
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Wilson, James H. "The QED-physical theory of electron spin and quantum entanglement." Physics Essays 35, no. 1 (November 1, 2022): 5–14. http://dx.doi.org/10.4006/0836-1398-35.1.5.
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The QED-Physical (QED-P) theory described in four previous papers [J. H. Wilson, Phys. Essays 28, 1 (2015); 29, 402 (2016); 31, 59 (2018); 34, 17 (2021)] is combined with QED into a single theory in this paper, since both are based on the same Dirac Equation four current c(α,I). QED couples this four-vector with an external electromagnetic (EM) field and uses covariant perturbation theory to produce results that are very accurate computationally [M. L. Eides et al., Phys. Rep. 342, 63 (2001)], except for the electron self-energy, which is infinite. The reason for QED’s accuracy is its Dirac equation velocity operator, cα, with highly unusual properties compared to classical velocity vectors. QED could not produce highly accurate answers without the 4 × 4 complex matrix cα as the electron “velocity operator.” QED-P starts with the same Dirac Equation four current used so successfully in QED, and the discrete internal spatial and time coordinate operators (ISaTCOs) are derived in QED-P to give the electron internal structure a very specific, but highly, nonclassical geometric description with no ad hoc assumptions. The QED/QED-physical (QED-P) unification theorem is stated and proved in Sec. VII. However, one should ask what new physical measurements are predicted by QED-P that are not determined by the very accurate QED? The answer is none yet, due to the very rapid fluctuation of the ISaTCOs with a period of ∼6.4 × 10−22 s. This induced electron field fluctuation is in addition to any vacuum fluctuation that exists without the electron field present. This paper presents a highly speculative, but testable, experiment, in which the ISaTCO rapid fluctuations may be confirmed indirectly as the physical basis of field quantum entanglement (QE). The electron’s ISaTCO produce a digital internal clock that’s locked out of phase with its entangled positron, and they communicate spin states at the phase speed of 2c2/vCoM. The communication of spin state information is instantaneous for vCoM = 0 but “slows down” to 4c at vCoM = 0.5c, still very fast.
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LI, CHE-MING, LI-YI HSU, and DER-SAN CHUU. "QUANTUM SECRET ENCRYPTION AND DECRYPTION IN CAVITY QED." International Journal of Quantum Information 07, no. 03 (April 2009): 681–87. http://dx.doi.org/10.1142/s0219749909003500.
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We present a proposal of the quantum secret encryption, transmission, and decryption implementation for quantum secret-sharing protocol using cavity QED. In the proposed scheme, the information is stored in two identical two-level atoms, and the two-qubit logic transformation is realized through the interaction between atoms and a nonresonant cavity mode. The proposed scheme requires no ancilla states to assist the intermediate atomic transitions and conditional quantum dynamics for quantum phase flip and quantum state diffusion. The encryption and decryption of quantum states are mostly governed by the Hamiltonian of an atom-cavity system. Moreover, secret transmission using quasi-swap gates for entanglement swapping has also been presented. With fewer supplements of external fields, a speed quantum protocol can be realized without universal gates.
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Cesário, André T., Diego L. B. Ferreira, Tiago Debarba, Fernando Iemini, Thiago O. Maciel, and Reinaldo O. Vianna. "Quantum Statistical Complexity Measure as a Signaling of Correlation Transitions." Entropy 24, no. 8 (August 19, 2022): 1161. http://dx.doi.org/10.3390/e24081161.
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We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signaling function of quantum order–disorder transitions. We discuss the possibility for such transitions to characterize interesting physical phenomena, as quantum phase transitions, or abrupt variations in correlation distributions. We apply our measure on two exactly solvable Hamiltonian models: the 1D-Quantum Ising Model (in the single-particle reduced state), and on Heisenberg XXZ spin-1/2 chain (in the two-particle reduced state). We analyze its behavior across quantum phase transitions for finite system sizes, as well as in the thermodynamic limit by using Bethe Ansatz technique.
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Levy, Liron, and Moshe Goldstein. "Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain." Universe 5, no. 1 (January 17, 2019): 33. http://dx.doi.org/10.3390/universe5010033.
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In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, and find that disorder may enhance the topological phase, and lead to the appearance of Majorana zero modes in systems whose clean version is trivial.
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HARSHMAN, N. L. "DYNAMICAL ENTANGLEMENT IN PARTICLE SCATTERING." International Journal of Modern Physics A 20, no. 27 (October 30, 2005): 6220–28. http://dx.doi.org/10.1142/s0217751x05029241.
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This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an S-matrix that respects certain symmetries and the entanglement of the pure out-state is measured. The analysis is phrased in terms of unitary, irreducible representations (UIRs) of the symmetry group in question, either the rotation group for the spin degrees of freedom or the Galilean group for non-relativistic particles. Entanglement may occurs when multiple UIRs appear in the direct sum decomposition of the direct product in-state, but it also depends of the scattering phase shifts.
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Martini, Francesco De, and Giovanni Di Giuseppe. "Multiparticle Quantum Superposition and Stimulated Entanglement by Parity Selective Amplification of Entangled States." Zeitschrift für Naturforschung A 56, no. 1-2 (February 1, 2001): 61–66. http://dx.doi.org/10.1515/zna-2001-0110.
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AbstractA multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the validity of the standard quantum theory for systems of increasing complexity, in a quasi decoherence-free environment. Because of its nonlocal structure the new system is expected to play a relevant role in the modem endeavor on quantum information and in the basic physics of entanglement. - Pacs: 03.65.Bz, 03.67.-a, 42.50.Ar, 89.70.+C
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Zurek, Wojciech Hubert. "Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons." Entropy 24, no. 11 (October 24, 2022): 1520. http://dx.doi.org/10.3390/e24111520.
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Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the `quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.
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Stephen, David T., Hendrik Poulsen Nautrup, Juani Bermejo-Vega, Jens Eisert, and Robert Raussendorf. "Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter." Quantum 3 (May 20, 2019): 142. http://dx.doi.org/10.22331/q-2019-05-20-142.
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Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lower-dimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.
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Wang, Jinzhao. "The refined quantum extremal surface prescription from the asymptotic equipartition property." Quantum 6 (February 16, 2022): 655. http://dx.doi.org/10.22331/q-2022-02-16-655.
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Information-theoretic ideas have provided numerous insights in the progress of fundamental physics, especially in our pursuit of quantum gravity. In particular, the holographic entanglement entropy is a very useful tool in studying AdS/CFT, and its efficacy is manifested in the recent black hole page curve calculation. On the other hand, the one-shot information-theoretic entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT. They are however more fundamental entropy measures from the quantum information perspective and should also play pivotal roles in holography. We combine the technical methods from both quantum information and quantum gravity to put this idea on firm grounds. In particular, we study the quantum extremal surface (QES) prescription that was recently revised to highlight the significance of one-shot entropies in characterizing the QES phase transition. Motivated by the asymptotic equipartition property (AEP), we derive the refined quantum extremal surface prescription for fixed-area states via a novel AEP replica trick, demonstrating the synergy between quantum information and quantum gravity. We further prove that, when restricted to pure bulk marginal states, such corrections do not occur for the higher Rényi entropies of a boundary subregion in fixed-area states, meaning they always have sharp QES transitions. Our path integral derivation suggests that the refinement applies beyond AdS/CFT, and we confirm it in a black hole toy model by showing that the Page curve, for a black hole in a superposition of two radiation stages, receives a large correction that is consistent with the refined QES prescription.
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RAMÓN MEDRANO, M., and N. G. SÁNCHEZ. "SEMICLASSICAL AND QUANTUM BLACK HOLES AND THEIR EVAPORATION, DE SITTER AND ANTI-DE SITTER REGIMES, GRAVITATIONAL AND STRING PHASE TRANSITIONS." International Journal of Modern Physics A 22, no. 32 (December 30, 2007): 6089–131. http://dx.doi.org/10.1142/s0217751x07038669.
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An effective string theory in physically relevant cosmological and black hole space–times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and anti-de Sitter AdS space–times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square-root branch point singularity in any space–time dimensions. This is of the type of the de Vega–Sánchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For dS background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition. (iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in nonthermal pure quantum radiation (no information loss). (vi) New lower string bounds are given for the Kerr–Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical–quantum (wave–particle) duality, which is universal irrespective of any symmetry or isommetry of the space–time and of the number or the kind of space–time dimensions.
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Wang, Ming-Ming, and Zhi-Guo Qu. "Weak measurement for improving the efficiency of remote state preparation in noisy." Quantum Information and Computation 18, no. 11&12 (September 2018): 975–87. http://dx.doi.org/10.26421/qic18.11-12-6.
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Quantum communication provides a new way for transmitting highly sensitive information. But the existence of quantum noise inevitably affects the security and reliability of a quantum communication system. The technique of weak measurement and its reversal measurement (WMRM) has been proposed to suppress the effect of quantum noise, especially, the amplitude-damping noise. Taking a GHZ based remote state preparation (RSP) scheme as an example, we discuss the effect of WMRM for suppressing four types of quantum noise that usually encountered in real-world, i.e., not only the amplitude-damping noise, but also the bit-flip, phase-flip (phase-damping) and depolarizing noise. And we give a quantitative study on how much a quantum output state can be improved by WMRM in noisy environment. It is shown that the technique of WMRM has certain effect for improving the fidelity of the output state in the amplitude-damping noise, and only has little effect for suppressing the depolarizing noise, while has no effect for suppressing the bit-flip and phase-flip (phase-damping) noise. Our result is helpful for improving the efficiency of entanglement-based quantum communication systems in real implementation.
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Cushman, Richard, and Jędrzej Śniatycki. "Classical and Quantum Spherical Pendulum." Symmetry 14, no. 3 (February 28, 2022): 496. http://dx.doi.org/10.3390/sym14030496.
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The seminal paper by Niels Bohr followed by a paper by Arnold Sommerfeld led to a revolutionary Bohr–Sommerfeld theory of atomic spectra. We are interested in the information about the structure of quantum mechanics encoded in this theory. In particular, we want to extend Bohr–Sommerfeld theory to a full quantum theory of completely integrable Hamiltonian systems, which is compatible with geometric quantization. In the general case, we use geometric quantization to prove analogues of the Bohr–Sommerfeld quantization conditions for the prequantum operators Pf. If a prequantum operator Pf satisfies the Bohr–Sommerfeld conditions and if it restricts to a directly quantized operator Qf in the representation corresponding to the polarization F, then Qf also satisfies the Bohr–Sommerfeld conditions. The proof that the quantum spherical pendulum is a quantum system of the type we are looking for requires a new treatment of the classical action functions and their properties. For the sake of completeness we have provided an extensive presentation of the classical spherical pendulum. In our approach to Bohr–Sommerfeld theory, which we call Bohr–Sommerfeld–Heisenberg quantization, we define shifting operators that provide transitions between different quantum states. Moreover, we relate these shifting operators to quantization of functions on the phase space of the theory. We use Bohr–Sommerfeld–Heisenberg theory to study the properties of the quantum spherical pendulum, in particular, the boundary conditions for the shifting operators and quantum monodromy.
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Aquilanti, Vincenzo, Nayara Dantas Coutinho, and Valter Henrique Carvalho-Silva. "Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2092 (March 20, 2017): 20160201. http://dx.doi.org/10.1098/rsta.2016.0201.
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This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto–Tsallis statistical weights: these generalize the Boltzmann–Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super -Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub -Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti -Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’.
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Han, Ya-Shuai, Xiao Zhang, Zhao Zhang, Jun Qu, and Jun-Min Wang. "Analysis of squeezed light source in band of alkali atom transitions based on cascaded optical parametric amplifiers." Acta Physica Sinica 71, no. 7 (2022): 074202. http://dx.doi.org/10.7498/aps.71.20212131.
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The squeezed light field in the band of alkali metal atomic transitions is an important quantum resource in the field of quantum information and precision measurement. The wavelengths of atomic transition lines (760–860 nm) are relatively short. Limited by the gray-tracking effect of nonlinear crystals, the squeezing degree of the squeezed light in this band generated by the optical parametric amplifiers is low. Now, the squeezing is about 3–5 dB. Considering the problems in the experimental generation of the squeezed light at the wavelengths of atomic transitions, the variation law of quantum noise of the light field output from the single optical parametric amplifier with its physical parameters is studied theoretically, and the optimal physical parameters are obtained. To further improve the squeezing in the band of alkali metal atomic transitions, the cascaded optical parametric amplifiers are considered. Based on the basic theory of the optical parametric amplifiers, the theoretical model of the cascaded optical parametric amplifiers is constructed, in which the optical loss and phase noise of the cascaded optical loops are considered. Based on this, the quantum noise characteristics of the light field output from the cascaded system versus the optical loss and phase noise are analyzed at the frequencies of 2 MHz and 100 kHz, respectively. It is found that for the squeezing at 2 MHz, cascading 2 to 3 optical parametric amplifiers can significantly improve the squeezing under the premise of the low optical path loss and phase noise; for the squeezing in the low-frequency band, the enhancement of the squeezing for the cascaded system is quite weak. Under the current experimental parameters, the squeezing at 2 MHz of the squeezed light on rubidium resonance can be improved from –5 dB to –7 dB by cascading another DOPA. For the squeezing at low frequency band, the cascaded system proves to be useless, and the efforts should be made to reduce the technique noise in the low frequency band. Furthermore, the quantum limit and spectral characteristics of the squeezed light field output from the cascaded system are further explored. This study can provide reference and guidance for the improvement in the squeezing degree of the band of atomic transitions.
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Poznanski, Roman, Eda Alemdar, Cacha Lleuvelyn, Gerry Leisman, and Erkki Brandas. "Journal of Multiscale Neuroscience." Journal of Multiscale Neuroscience 2, no. 1 (April 28, 2023): 159–69. http://dx.doi.org/10.56280/1560617630.
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This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.
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Alemdar, Eda, Roman Poznanski, Roman Poznanski, Lleuvelyn Cacha, Gerry Leisman, and Erkki Brandas. "Journal of Multiscale Neuroscience." Journal of Multiscale Neuroscience 2, no. 1 (April 28, 2023): 159–69. http://dx.doi.org/10.56280/1561870661.
Full textAbstract:
This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.
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A.V, Yudenkov, Terentyev S.E., and Kovaleva A.E. "Informational Description of Systemic Crises." International Journal of Engineering & Technology 7, no. 4.36 (December 9, 2018): 899. http://dx.doi.org/10.14419/ijet.v7i4.36.24917.
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The paper studies the possibility of determining and classifying the crisis as a complex system by a remote observer on the basis of subjective information. Description and analysis of complex systems is a fundamentally unsolvable problem. However, there may be a partial solution to the problem through the use of multilevel modeling. Therefore, the development of new fairly common methods for modeling complex systems is an urgent task. The aim of the work is to develop fairly common methods of modeling complex systems in crisis. For this purpose, the evolution of the system is considered at three levels: micro level, meso level and macro level. At the micro level such concepts as unit of information, growth of information are considered. At the macro level, two models describing system crises are proposed. The simulation is based on stochastic differential equations and the theory of phase transitions. At the micro level, the process of transition from one stable state to another is studied. It is assumed that the remote macroscopic observer receives information about the evolution of the system. The new results include the following. A new interpretation of information from the quantum-statistical point of view. Unlike Shannon’s information in this paper, the information is associated with the phase space of the system. This makes it possible to apply basic physical and mathematical methods to the study of the evolution of different nature of systems. An analogue of the second principle of thermodynamics at the micro level-the principle of maximum information is obtained. The obtained results allowed justifying the use of Langevin equations for crisis modeling, as well as to obtain an analogy between the types of crises and phase transitions. The paper considers illustrating examples of complex systems in the process of transition from one stable state to another.
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Bharti, Kishor, Maharshi Ray, and Leong-Chuan Kwek. "Non-Classical Correlations in n-Cycle Setting." Entropy 21, no. 2 (February 1, 2019): 134. http://dx.doi.org/10.3390/e21020134.
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Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen–Specker–Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu–Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.
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Luchnikov, Ilia A., Alexander Ryzhov, Pieter-Jan Stas, Sergey N. Filippov, and Henni Ouerdane. "Variational Autoencoder Reconstruction of Complex Many-Body Physics." Entropy 21, no. 11 (November 7, 2019): 1091. http://dx.doi.org/10.3390/e21111091.
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Thermodynamics is a theory of principles that permits a basic description of the macroscopic properties of a rich variety of complex systems from traditional ones, such as crystalline solids, gases, liquids, and thermal machines, to more intricate systems such as living organisms and black holes to name a few. Physical quantities of interest, or equilibrium state variables, are linked together in equations of state to give information on the studied system, including phase transitions, as energy in the forms of work and heat, and/or matter are exchanged with its environment, thus generating entropy. A more accurate description requires different frameworks, namely, statistical mechanics and quantum physics to explore in depth the microscopic properties of physical systems and relate them to their macroscopic properties. These frameworks also allow to go beyond equilibrium situations. Given the notably increasing complexity of mathematical models to study realistic systems, and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models show limitations in scope or applicability. On the other hand, machine learning, i.e., data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks, in particular, have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE)—a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show, with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.
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Sulay, Rehin, Anandhu Krishnan, Balasubramoniam Muralikrishna, Sudheesh Devadas, Chandralekha Rajalakshmi, Jintumol Mathew, and Vibin Ipe Thomas. "A Quantum Chemical Investigation into the Molecular Mechanism of the Atmospheric Reactions of Chemi-Ions with Nitrogen and Nitrogen Oxides." Entropy 24, no. 9 (September 7, 2022): 1257. http://dx.doi.org/10.3390/e24091257.
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Nitrogen oxides and chemi-ions are atmospheric pollutants with considerable aeronomic interest. These toxicants can react with each other, producing various ionic species and highly reactive by-products that play a crucial role in aerosol clustering and mediate several important atmospheric reactions. Understanding the chemical reactivity of these pollutants can provide essential information for controlling their excess emission into the atmosphere. Computational modeling and electronic structure studies help in predicting the structure, reactivity, and thermodynamics of transient atmospheric chemical species and can guide experimental research by providing vital mechanistic insights and data. In the present study, a computational investigation into the mechanisms of the binary associative reactions between negative ions: O2− and O3− with NO, NO2, and N2 was conducted using the Coupled-Cluster Singles and Doubles (CCSD) theory. Five model reactions between N2/NOx with On− (n = 2, 3) were considered in this work. Our calculations revealed that reactions (2) and (5) are two sequential processes involving intermediates, and all others occur in a concerted manner by direct transitions from the reactants to the products, with no isolable intermediates proceeding via single non-planar transition states. Our study revealed that the higher activation barrier required for the formation of NO3− (2) as compared to NO2− (1) could be the reason for the excess formation of NO2− ions over NO3− ions in the atmosphere. Further, all the investigated reactions except (5) are found to be feasible at room temperature. The energy required to break N-N bonds in the N2 molecule justifies the high barrier for (5). The results obtained from the study are in close agreement with the available experimental data. Moreover, the data from the study can be utilized for the evaluation of experiments and model predictions pertaining to NOx oxidation and molecular modeling of the gas-phase chemistry of pollutants/nucleation precursors formed in the Earth’s atmosphere and aircraft engines.
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Liu, Peng, Chao Niu, Zi-Jian Shi, and Cheng-Yong Zhang. "Entanglement wedge minimum cross-section in holographic massive gravity theory." Journal of High Energy Physics 2021, no. 8 (August 2021). http://dx.doi.org/10.1007/jhep08(2021)113.
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Abstract We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By comparing the quantum information behavior in the thermodynamic phase transition of holographic superconductors, we analyze the relationship and difference between them and provide two mechanisms of quantum information scaling behavior in the thermodynamic phase transition.
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Sotnikov, O. M., I. A. Iakovlev, A. A. Iliasov, M. I. Katsnelson, A. A. Bagrov, and V. V. Mazurenko. "Certification of quantum states with hidden structure of their bitstrings." npj Quantum Information 8, no. 1 (April 22, 2022). http://dx.doi.org/10.1038/s41534-022-00559-7.
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AbstractThe rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozens of qubits, which poses a strong demand on efficient methods for characterization and verification of large-scale quantum states. Here, we propose a numerically cheap procedure to distinguish quantum states which is based on a limited number of projective measurements in at least two different bases and computing inter-scale dissimilarities of the resulting bit-string patterns via coarse-graining. The information one obtains through this procedure can be viewed as a ‘hash function’ of quantum state—a simple set of numbers which is specific for a concrete wave function and can be used for certification. We show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. Our approach can also be employed to detect phase transitions in quantum magnetic systems.
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Bagrov, Andrey A., Mikhail Danilov, Sergey Brener, Malte Harland, Alexander I. Lichtenstein, and Mikhail I. Katsnelson. "Detecting quantum critical points in the t-$$t'$$ Fermi-Hubbard model via complex network theory." Scientific Reports 10, no. 1 (November 24, 2020). http://dx.doi.org/10.1038/s41598-020-77513-0.
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AbstractA considerable success in phenomenological description of $$\text {high-T}_{\text{c}}$$ high-T c superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)—a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-$$t'$$ t ′ Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-$$t'$$ t ′ Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.
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Wu, L. A., M. S. Sarandy, D. A. Lidar, and L. J. Sham. "Linking entanglement and quantum phase transitions via density-functional theory." Physical Review A 74, no. 5 (November 27, 2006). http://dx.doi.org/10.1103/physreva.74.052335.
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Castaños, Octavio, Sergio Cordero, Ramón López-Peña, and Eduardo Nahmad-Achar. "Geometry, quantum correlations, and phase transitions in the Λ-atomic configuration." Journal of Physics A: Mathematical and Theoretical, November 28, 2022. http://dx.doi.org/10.1088/1751-8121/aca6bb.
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Abstract The quantum phase diagram for a finite 3-level system in the Λ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of the system. These concepts are calculated for both, the symmetry-adapted variational coherent states and the numerical diagonalisation of the Hamiltonian, and compared. The differences in purity and entanglement obtained in both calculations can be explained and visualised by means of this simplex representation.
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"A Two-step Creation of Phonon Entanglement with Quantized Light." JPS Hot Topics 1 (2021). http://dx.doi.org/10.7566/jpsht.1.066.
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Dynamics of photoinduced quantum entanglement generation between phonons is theoretically revealed. The results contribute to the study of fundamental theoretical problems within quantum dynamics of photoinduced phase transitions and quantum information science.
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"Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory." JPS Hot Topics 1 (2021). http://dx.doi.org/10.7566/jpsht.1.063.
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Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.
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M. Oliveira, Miguel, Pedro Ribeiro, and Stefan Kirchner. "Efficient quantum information probes of nonequilibrium quantum criticality." npj Quantum Information 9, no. 1 (January 13, 2023). http://dx.doi.org/10.1038/s41534-022-00671-8.
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AbstractQuantum information-based approaches, in particular the fidelity, have been flexible probes for phase boundaries of quantum matter. A major hurdle to a more widespread application of fidelity and other quantum information measures to strongly correlated quantum materials is the inaccessibility of the fidelity susceptibility to most state-of-the-art numerical methods. This is particularly apparent away from equilibrium where, at present, no general critical theory is available and many standard techniques fail. Motivated by the usefulness of quantum information-based measures we show that a widely accessible quantity, the single-particle affinity, is able to serve as a versatile instrument to identify phase transitions beyond Landau’s paradigm. We demonstrate that it not only is able to signal previously identified nonequilibrium phase transitions but also has the potential to detect hitherto unknown phases in models of quantum matter far from equilibrium.
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Ham, Byoung S. "Macroscopic and deterministic quantum feature generation via phase basis quantization in a cascaded interferometric system." Scientific Reports 11, no. 1 (September 24, 2021). http://dx.doi.org/10.1038/s41598-021-98478-8.
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AbstractQuantum entanglement is the quintessence of quantum information science governed by quantum superposition mostly limited to a microscopic regime. For practical applications, however, macroscopic entanglement has an essential benefit for quantum sensing and metrology to beat its classical counterpart. Recently, a coherence approach for entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where the quantum feature of entanglement has been achieved via phase basis superposition between identical interferometric systems. Such a coherence method is based on the wave nature of a photon without violating quantum mechanics under the complementarity theory. Here, a method of phase basis quantization via phase basis superposition is presented for macroscopic entanglement in an interferometric system, which is corresponding to the energy quantization of a photon.
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Antonini, Stefano, Brianna Grado-White, Shao-Kai Jian, and Brian Swingle. "Holographic measurement and quantum teleportation in the SYK thermofield double." Journal of High Energy Physics 2023, no. 2 (February 9, 2023). http://dx.doi.org/10.1007/jhep02(2023)095.
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Abstract According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model’s thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.
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Nahum, Adam, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman. "Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory." PRX Quantum 2, no. 1 (March 30, 2021). http://dx.doi.org/10.1103/prxquantum.2.010352.
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Dong, Xi, Sean McBride, and Wayne W. Weng. "Replica wormholes and holographic entanglement negativity." Journal of High Energy Physics 2022, no. 6 (June 2022). http://dx.doi.org/10.1007/jhep06(2022)094.
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Abstract Recent work has shown how to understand the Page curve of an evaporating black hole from replica wormholes. However, more detailed information about the structure of its quantum state is needed to fully understand the dynamics of black hole evaporation. Here we study entanglement negativity, an important measure of quantum entanglement in mixed states, in a couple of toy models of evaporating black holes. We find four phases dominated by different types of geometries: the disconnected, cyclically connected, anti-cyclically connected, and pairwise connected geometries. The last of these geometries are new replica wormholes that break the replica symmetry spontaneously. We also analyze the transitions between these four phases by summing more generic replica geometries using a Schwinger-Dyson equation. In particular, we find enhanced corrections to various negativity measures near the transition between the cyclic and pairwise phase.
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Li, Wei, Le Wang, and Shengmei Zhao. "Phase Matching Quantum Key Distribution based on Single-Photon Entanglement." Scientific Reports 9, no. 1 (October 29, 2019). http://dx.doi.org/10.1038/s41598-019-51848-9.
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Abstract Two time-reversal quantum key distribution (QKD) schemes are the quantum entanglement based device-independent (DI)-QKD and measurement-device-independent (MDI)-QKD. The recently proposed twin field (TF)-QKD, also known as phase-matching (PM)-QKD, has improved the key rate bound from O(η) to O$$(\sqrt{{\boldsymbol{\eta }}})$$ ( η ) with η the channel transmittance. In fact, TF-QKD is a kind of MDI-QKD but based on single-photon detection. In this paper, we propose a different PM-QKD based on single-photon entanglement, referred to as single-photon entanglement-based phase-matching (SEPM)-QKD, which can be viewed as a time-reversed version of the TF-QKD. Detection loopholes of the standard Bell test, which often occur in DI-QKD over long transmission distances, are not present in this protocol because the measurement settings and key information are the same quantity which is encoded in the local weak coherent state. We give a security proof of SEPM-QKD and demonstrate in theory that it is secure against all collective attacks and beam-splitting attacks. The simulation results show that the key rate enjoys a bound of O$$(\sqrt{{\boldsymbol{\eta }}})$$ ( η ) with respect to the transmittance. SEPM-QKD not only helps us understand TF-QKD more deeply, but also hints at a feasible approach to eliminate detection loopholes in DI-QKD for long-distance communications.
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Guerrero, Julio, Alberto Mayorgas, and Manuel Calixto. "Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin–Meshkov–Glick D-level atom models." Quantum Information Processing 21, no. 6 (June 2022). http://dx.doi.org/10.1007/s11128-022-03524-7.
Full textAbstract:
AbstractIn this paper we pursue the use of information measures (in particular, information diagrams) for the study of entanglement in symmetric multi-quDit systems. We use generalizations to $${U}(D)$$ U ( D ) of spin $${U}(2)$$ U ( 2 ) coherent states and their adaptation to parity (multicomponent Schrödinger cats), and we analyse one- and two-quDit reduced density matrices. We use these correlation measures to characterize quantum phase transitions occurring in Lipkin–Meshkov–Glick models of $$D=3$$ D = 3 -level identical atoms, and we propose the rank of the corresponding reduced density matrix as a discrete order parameter.