Journal articles: 'Open quantum systems, quantum-to-classical crossover'

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RUGGIERO, B., V. CORATO, E. ESPOSITO, C. GRANATA, M. RUSSO, P. SILVESTRINI, and L. STODOLSKY. "MACROSCOPIC QUANTUM COHERENCE IN JOSEPHSON SYSTEMS." International Journal of Modern Physics B 14, no. 25n27 (October 30, 2000): 3050–55. http://dx.doi.org/10.1142/s0217979200003290.

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We present our recent experiments on macroscopic tunneling in the quantum regime for underdamped Josephson junctions with different classical-quantum crossover temperatures. These experiments are performed towards the observation of macroscopic quantum coherence in Josephson systems. A new method to measure coherence in a two-level system based on the adiabatic inversion in an rf squid, is presented. This approach could open new perspectives in view of realization of an elementary quantum bit.

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Wu, W. J., K. Yan, Y. Q. Xie, Yinzhong Wu, and Xiang Hao. "Quantum speed-up dynamical crossover in open systems." International Journal of Quantum Information 15, no. 04 (June 2017): 1750027. http://dx.doi.org/10.1142/s0219749917500277.

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We put forward a measure for evaluating quantum speed limit for arbitrary mixed states of open systems by means of trace distance. Compared with some present measures, it can provide an optimal bound to the speed of the evolution. The dynamical crossover from no speedup region to speedup region happens during the spontaneous decay of an atom. The evolution is characteristic of the alternating behavior between quantum acceleration and deceleration in the strong coupling case. Under the condition of detuning, the evolution can be initially accelerated and then decelerated to a normal process either in the weak or strong coupling regime. In accordance with the uncertainty relation, we demonstrate that the potential capacity for quantum speedup evolution is closely related to the energy feedback from the reservoir to the system. The negative decay rate for the evolution results in the speedup process where the photons previously emitted by the atom are reabsorbed at a later time. The values of the spontaneous decay rate become positive after a long enough time, which results in the evolution with no speedup potential.

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da Silva, L. D., C. A. Batista, I. R. R. González, A. M. S. Macêdo, W. R. de Oliveira, and S. B. Melo. "A Discrete Exterior Calculus Approach to Quantum Transport and Quantum Chaos on Surface." Journal of Computational and Theoretical Nanoscience 16, no. 9 (September 1, 2019): 3670–82. http://dx.doi.org/10.1166/jctn.2019.8364.

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We address the problem of computing transport observables and spectral characteristics of quantum dynamics on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to both open and closed quantum systems. We present an efficient algorithm for the calculation of the recursive Green’s functions (for open systems) and the full set of eigenfunctions and eigenvalues (for closed systems) using numerical tools available for DEC. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs and to obtain the spectra of ballistic cavities defined on curved surfaces. In both cases we found numerical evidences of a curvature induced integrable-chaotic crossover.

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Abasto, D. F., M. Mohseni, S. Lloyd, and P. Zanardi. "Exciton diffusion length in complex quantum systems: the effects of disorder and environmental fluctuations on symmetry-enhanced supertransfer." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1972 (August 13, 2012): 3750–70. http://dx.doi.org/10.1098/rsta.2011.0213.

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Symmetric couplings among aggregates of n chromophores increase the transfer rate of excitons by a factor n 2 , a quantum-mechanical phenomenon called ‘supertransfer’. In this work, we demonstrate how supertransfer effects induced by geometrical symmetries can enhance the exciton diffusion length by a factor n along cylindrically symmetric structures, consisting of arrays of rings of chromophores, and along spiral arrays. We analyse both closed-system dynamics and open quantum dynamics, modelled by combining a random bosonic bath with static disorder. In the closed-system case, we use the symmetries of the system within a short-time approximation to obtain a closed analytical expression for the diffusion length that explicitly reveals the supertransfer contribution. When subject to disorder, we show that supertransfer can enhance excitonic diffusion lengths for small disorders and characterize the crossover from coherent to incoherent motion. Owing to the quasi-one-dimensional nature of the model, disorder ultimately localizes the excitons, diminishing but not destroying the effects of supertransfer. When dephasing effects are included, we study the scaling of diffusion with both time and number of chromophores and observe that the transition from a coherent, ballistic regime to an incoherent, random-walk regime occurs at the same point as the change from supertransfer to classical scaling.

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Paz, Daniel A., and Mohammad F. Maghrebi. "Driven-dissipative Ising model: Dynamical crossover at weak dissipation." Europhysics Letters 136, no. 1 (October 1, 2021): 10002. http://dx.doi.org/10.1209/0295-5075/ac33cb.

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Abstract Driven quantum systems coupled to an environment typically exhibit effectively thermal behavior with relaxational dynamics near criticality. However, a different qualitative behavior might be expected in the weakly dissipative limit due to the competition between coherent dynamics and weak dissipation. In this work, we investigate a driven-dissipative infinite-range Ising model in the presence of individual atomic dissipation, a model that emerges from the paradigmatic open Dicke model in the large-detuning limit. We show that the system undergoes a dynamical crossover from relaxational dynamics, with a characteristic dynamical exponent , to underdamped critical dynamics governed by the exponent in the weakly dissipative regime; a behavior that is markedly distinct from that of equilibrium. Finally, utilizing an exact diagrammatic representation, we demonstrate that the dynamical crossover to underdamped criticality is not an artifact of the mean-field nature of the model and persists even in the presence of short-range perturbations.

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Agam, Oded, Igor Aleiner, and Anatoly Larkin. "Shot Noise in Chaotic Systems: “Classical” to Quantum Crossover." Physical Review Letters 85, no. 15 (October 9, 2000): 3153–56. http://dx.doi.org/10.1103/physrevlett.85.3153.

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Warszawski, Prahlad, and Howard M. Wiseman. "Open quantum systems are harder to track than open classical systems." Quantum 3 (October 7, 2019): 192. http://dx.doi.org/10.22331/q-2019-10-07-192.

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For a Markovian (in the strongest sense) open quantum system it is possible, by continuously monitoring the environment, to perfectly track the system; that is, to know the stochastically evolving pure state of the system without altering the master equation. In general, even for a system with a finite Hilbert space dimension D, the pure state trajectory will explore an infinite number of points in Hilbert space, meaning that the dimension K of the classical memory required for the tracking is infinite. However, Karasik and Wiseman [Phys. Rev. Lett., 106(2):020406, 2011] showed that tracking of a qubit (D=2) is always possible with a bit (K=2), and gave a heuristic argument implying that a finite K should be sufficient for any D, although beyond D=2 it would be necessary to have K>D. Our paper is concerned with rigorously investigating the relationship between D and Kmin, the smallest feasible K. We confirm the long-standing conjecture of Karasik and Wiseman that, for generic systems with D>2, Kmin>D, by a computational proof (via Hilbert Nullstellensatz certificates of infeasibility). That is, beyond D=2, D-dimensional open quantum systems are provably harder to track than D-dimensional open classical systems. We stress that this result allows complete freedom in choice of monitoring scheme, including adaptive monitoring which is, in general, necessary to implement a physically realizable ensemble (as it is known) of just K pure states. Moreover, we develop, and better justify, a new heuristic to guide our expectation of Kmin as a function of D, taking into account the number L of Lindblad operators as well as symmetries in the problem. The use of invariant subspace and Wigner symmetries (that we recently introduced elsewhere, [New J. Phys. https://doi.org/10.1088/1367-2630/ab14b2]) makes it tractable to conduct a numerical search, using the method of polynomial homotopy continuation, to find finite physically realizable ensembles in D=3. The results of this search support our heuristic. We thus have confidence in the most interesting feature of our heuristic: in the absence of symmetries, Kmin∼D2, implying a quadratic gap between the classical and quantum tracking problems. Explicit adaptive monitoring schemes that realize the discovered finite ensembles are obtained numerically, thus facilitating future experimental investigations.

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Sereni, J. G. "Crossover from classical to quantum regime in Ce-lattice systems." Physica B: Condensed Matter 398, no. 2 (September 2007): 412–15. http://dx.doi.org/10.1016/j.physb.2007.04.050.

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Schomerus, Henning, and Philippe Jacquod. "Quantum-to-classical correspondence in open chaotic systems." Journal of Physics A: Mathematical and General 38, no. 49 (November 22, 2005): 10663–82. http://dx.doi.org/10.1088/0305-4470/38/49/013.

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Klimontovich, Yu L. "From Classical to Quantum Theory of Open Systems." Physica Scripta 61, no. 1 (January 1, 2000): 17–31. http://dx.doi.org/10.1238/physica.regular.061a00017.

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Dann, Roie, and Ronnie Kosloff. "Quantum thermo-dynamical construction for driven open quantum systems." Quantum 5 (November 25, 2021): 590. http://dx.doi.org/10.22331/q-2021-11-25-590.

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Quantum dynamics of driven open systems should be compatible with both quantum mechanic and thermodynamic principles. By formulating the thermodynamic principles in terms of a set of postulates we obtain a thermodynamically consistent master equation. Following an axiomatic approach, we base the analysis on an autonomous description, incorporating the drive as a large transient control quantum system. In the appropriate physical limit, we derive the semi-classical description, where the control is incorporated as a time-dependent term in the system Hamiltonian. The transition to the semi-classical description reflects the conservation of global coherence and highlights the crucial role of coherence in the initial control state. We demonstrate the theory by analyzing a qubit controlled by a single bosonic mode in a coherent state.

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Haase, J. F., A. Smirne, S. F. Huelga, J. Kołodynski, and R. Demkowicz-Dobrzanski. "Precision Limits in Quantum Metrology with Open Quantum Systems." Quantum Measurements and Quantum Metrology 5, no. 1 (August 1, 2016): 13–39. http://dx.doi.org/10.1515/qmetro-2018-0002.

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Abstract The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcomewhen using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment.We adopt a complementary approach,wherewe first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system’s dissipative time evolution.We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

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Takov, I. P. "Classical to quantum crossover of the critical behaviour of impure systems." Journal of Physical Studies 3, no. 4 (1999): 422–30. http://dx.doi.org/10.30970/jps.03.422.

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Osmanov, Maksym, and Hans Christian Öttinger. "Open Quantum Systems Coupled to Time-Dependent Classical Environments." International Journal of Thermophysics 34, no. 7 (June 8, 2013): 1255–64. http://dx.doi.org/10.1007/s10765-013-1466-3.

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WISEMAN, H. M. "FEEDBACK IN OPEN QUANTUM SYSTEMS." Modern Physics Letters B 09, no. 11n12 (May 20, 1995): 629–54. http://dx.doi.org/10.1142/s0217984995000590.

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Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

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Accardi, L., D. Chruściński, A. Kossakowski, T. Matsuoka, and M. Ohya. "On Classical and Quantum Liftings." Open Systems & Information Dynamics 17, no. 04 (December 2010): 361–87. http://dx.doi.org/10.1142/s1230161210000230.

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We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to 'lift' a state of a system into a state of 'system + reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so-called circulant states.

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Calvani, D., A. Cuccoli, N. I. Gidopoulos, and P. Verrucchi. "Parametric representation of open quantum systems and cross-over from quantum to classical environment." Proceedings of the National Academy of Sciences 110, no. 17 (April 9, 2013): 6748–53. http://dx.doi.org/10.1073/pnas.1217776110.

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BLANCHARD, PH, and R. OLKIEWICZ. "DECOHERENCE INDUCED TRANSITION FROM QUANTUM TO CLASSICAL DYNAMICS." Reviews in Mathematical Physics 15, no. 03 (May 2003): 217–43. http://dx.doi.org/10.1142/s0129055x03001631.

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Framework for a general discussion of environmentally induced classical properties, like superselection rules, privileged basis and classical behavior, in quantum systems with both finite and infinite number of degrees of freedom is proposed. A number of examples showing that classical properties do not have to be postulated as an independent ingredient are given. In particular, it is shown that infinite open quantum systems in some cases may behave like simple classical dynamical systems.

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Wu, W. J., K. Yan, Yinzhong Wu, and Xiang Hao. "Thermal quantum speed limit for classical-driving open systems." Modern Physics Letters B 30, no. 32n33 (November 30, 2016): 1650389. http://dx.doi.org/10.1142/s0217984916503899.

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Quantum speed limit (QSL) time for open systems driven by classical fields is studied in the presence of thermal bosonic environments. The decoherence process is quantitatively described by the time convolutionless master equation. The evolution speed of an open system can be accelerated by means of driving classical fields at finite temperatures. It is found out that the structural reservoir at low temperature may contribute to the acceleration of quantum evolution. The manifest oscillation of QSL time happens under the circumstance of classical driving field. The scaling property of QSL for entangled systems is also investigated. It is demonstrated that the entanglement of open systems can be considered as one kind of resource for improving the potential capacity of thermal quantum speedup.

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Blanchard, Ph, and R. Olkiewicz. "Decoherence, Classical Properties and Entanglement of Quantum Systems." Zeitschrift für Naturforschung A 56, no. 1-2 (February 1, 2001): 124–27. http://dx.doi.org/10.1515/zna-2001-0118.

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AbstractWe discuss the properties of decoherence and its role in the appearance of classical properties in open quantum systems. In particular, it is used for classification of pure states with respect to their ability to persist despite the environmental monitoring.

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CIVALLERI, PIER PAOLO, MARCO GILLI, and MICHELE BONNIN. "THE HARMONIC BALANCE TECHNIQUE ANALYSIS OF OPEN QUANTUM SYSTEMS." International Journal of Bifurcation and Chaos 18, no. 07 (July 2008): 1973–82. http://dx.doi.org/10.1142/s0218127408021488.

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The Harmonic Balance Technique (HBT) is used to analyze the steady state performance of a two-state quantum system interacting with a classical sinusoidal electromagnetic wave and with a thermal bath at a fixed temperature. The linear time-variant differential equations describing such a system can be solved to any number of harmonics and the results can be compared with those obtained with the classical RWA approximation, thus emphasizing the validity limits of the latter.

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Milburn, Gerard, and Sally Shrapnel. "Classical and Quantum Causal Interventions." Entropy 20, no. 9 (September 8, 2018): 687. http://dx.doi.org/10.3390/e20090687.

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Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in response to interventions on others. Recent work has generalised concepts from this field to situations involving quantum systems, resulting in a new notion of quantum causal structure. A key concept in both the classical and quantum context is that of an intervention. Interventions are the controlled operations required to identify causal structure and ultimately the feature that endows causal models with empirical meaning. Although interventions are a crucial feature of both the classical and quantum causal modelling frameworks, to date there has been no discussion of their physical basis. In this paper, we consider interventions from a physical perspective and show that, in both the classical and quantum case, they are constrained by the thermodynamics of measurement and feedback in open systems. We demonstrate that the perfect “atomic” or “surgical” interventions characterised by Pearl’s famous do-calculus are physically impossible, and this is the case for both classical and quantum systems.

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Iftikhar, Z., A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, and F. Pierre. "Tunable quantum criticality and super-ballistic transport in a “charge” Kondo circuit." Science 360, no. 6395 (May 3, 2018): 1315–20. http://dx.doi.org/10.1126/science.aan5592.

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Quantum phase transitions (QPTs) are ubiquitous in strongly correlated materials. However, the microscopic complexity of these systems impedes the quantitative understanding of QPTs. We observed and thoroughly analyzed the rich strongly correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. An unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly correlated phenomena.

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Vlasov, Sergei, Pavel F. Bessarab, Valery M. Uzdin, and Hannes Jónsson. "Classical to quantum mechanical tunneling mechanism crossover in thermal transitions between magnetic states." Faraday Discussions 195 (2016): 93–109. http://dx.doi.org/10.1039/c6fd00136j.

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Transitions between states of a magnetic system can occur by jumps over an energy barrier or by quantum mechanical tunneling through the energy barrier. The rate of such transitions is an important consideration when the stability of magnetic states is assessed for example for nanoscale candidates for data storage devices. The shift in transition mechanism from jumps to tunneling as the temperature is lowered is analyzed and a general expression derived for the crossover temperature. The jump rate is evaluated using a harmonic approximation to transition state theory. First, the minimum energy path for the transition is found with the geodesic nudged elastic band method. The activation energy for the jumps is obtained from the maximum along the path, a saddle point on the energy surface, and the eigenvalues of the Hessian matrix at that point as well as at the initial state minimum used to estimate the entropic pre-exponential factor. The crossover temperature for quantum mechanical tunneling is evaluated from the second derivatives of the energy with respect to orientation of the spin vector at the saddle point. The resulting expression is applied to test problems where analytical results have previously been derived, namely uniaxial and biaxial spin systems with two-fold anisotropy. The effect of adding four-fold anisotropy on the crossover temperature is demonstrated. Calculations of the jump rate and crossover temperature for tunneling are also made for a molecular magnet containing an Mn₄ group. The results are in excellent agreement with previously reported experimental measurements on this system.

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Nicolosi, S. "An Operator-Based Exact Treatment of Open Quantum Systems." Open Systems & Information Dynamics 12, no. 02 (June 2005): 163–77. http://dx.doi.org/10.1007/s11080-005-5727-x.

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Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. The theory of open quantum systems thus plays a major role in many applications of quantum physics since perfect isolation of quantum system is not possible and since a complete microscopic description or control of the environment degrees of freedom is not feasible or only partially so [1]. Practical considerations therefore force one to seek for a simpler, effectively probabilistic description in terms of an open system. There is a close physical and mathematical connection between the evolution of an open system, the state changes induced by quantum measurements, and the classical notion of a stochastic process. The paper provides a bibliographic review of this interrelations, it shows the mathematical equivalence between markovian master equation and generalized piecewise deterministic processes [1] and it introduces the open system in an open observed environment model.

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Arenas, Mallén, and Rolando Rebolledo. "Can One Validly Use Classical Statistical Inference in Open Quantum Systems?" Open Systems & Information Dynamics 17, no. 04 (December 2010): 311–30. http://dx.doi.org/10.1142/s1230161210000205.

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A major problem to perform statistical inference in open quantum systems is the perturbation induced by the measurement process. However, at least theoretically, a suitable choice of the measurement process could provide a consistent approach through classical stochastic processes. This work proposes a method to perform statistical inference on open quantum systems represented by quantum Markov semigroups having a suitable classical reduction. The method is based on measurements associated to observables generating invariant abelian algebras.

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Morimae, Tomoyuki. "Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof." Impact 2019, no. 10 (December 30, 2019): 30–32. http://dx.doi.org/10.21820/23987073.2019.10.30.

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In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

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Huppert, Simon, Thomas Plé, Sara Bonella, Philippe Depondt, and Fabio Finocchi. "Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths." Applied Sciences 12, no. 9 (May 9, 2022): 4756. http://dx.doi.org/10.3390/app12094756.

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This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.

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Li, Minggen, and Jingdong Bao. "Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems." Entropy 22, no. 8 (July 30, 2020): 839. http://dx.doi.org/10.3390/e22080839.

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We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.

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BENATTI, FABIO, and ROBERTO FLOREANINI. "OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT." International Journal of Modern Physics B 19, no. 19 (July 30, 2005): 3063–139. http://dx.doi.org/10.1142/s0217979205032097.

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We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

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Kendon, Vivien M., Kae Nemoto, and William J. Munro. "Quantum analogue computing." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1924 (August 13, 2010): 3609–20. http://dx.doi.org/10.1098/rsta.2010.0017.

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We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.

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Man’ko, Olga V., and Vladimir I. Man’ko. "Probability Representation of Quantum States." Entropy 23, no. 5 (April 29, 2021): 549. http://dx.doi.org/10.3390/e23050549.

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The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

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EVERITT, M. J. "NON-LINEAR DYNAMICS, ENTANGLEMENT AND THE QUANTUM-CLASSICAL CROSSOVER OF TWO COUPLED SQUID RINGS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4311–19. http://dx.doi.org/10.1142/s0217979209063468.

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We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.

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SARRIS, C. M., and A. N. PROTO. "THE SU(2) SEMI QUANTUM SYSTEMS DYNAMICS AND THERMODYNAMICS." International Journal of Modern Physics B 24, no. 25n26 (October 20, 2010): 5037–49. http://dx.doi.org/10.1142/s0217979210057183.

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The dynamical description of a semi quantum nonlinear systems whose classical limit is not chaotic is still an open question. These systems are characterized by mixing a classical system with a quantum-mechanical one. As some of them lead to an irregular dynamics, the name "semi quantum chaos" arises. In this contribution we study two different Hamiltonians through the Maximum Entropy Principle Approach (MEP). Taking advantage of the MEP formalism, it can be clearly established that the Hamiltonians belonging to the SU(2) Lie algebra have common properties and a common treatment can be developed for them. These Hamiltonians resemble a quantum spin system coupled to a classical cavity. In the present contribution, we show that all of them share the generalized uncertainty principle as an invariant of the motion and other invariants as well. Two different classical potentials V(q) have been studied. Their specific heat are evaluated in terms of the extensive (mean values) and the intensive (Lagrange multipliers) variables. The main result of the present contribution is to show that the specific heat of these systems can be fixed independently of the temperature by setting only the initial conditions on the extensive or intensive variables, as well as the value of the quantum-classical coupling parameter. It could be possible to infer that this result can be extended to generalized forms for the V(q) classical potential.

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Milburn, G. J. "Decoherence and the conditions for the classical control of quantum systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1975 (September 28, 2012): 4469–86. http://dx.doi.org/10.1098/rsta.2011.0487.

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We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalized in the diagonal basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalization is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are structurally similar to recently proposed models for consistently combining quantum and classical stochastic dynamics.

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36

XU, JIN-SHI, and CHUAN-FENG LI. "QUANTUM DISCORD UNDER SYSTEM–ENVIRONMENT COUPLING: THE TWO-QUBIT CASE." International Journal of Modern Physics B 27, no. 01n03 (November 26, 2012): 1345054. http://dx.doi.org/10.1142/s0217979213450549.

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Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system–environment dynamics of two-qubit quantum discord and the influence of initial system–environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.

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ISAR, A., A. SANDULESCU, and W. SCHEID. "PHASE SPACE REPRESENTATION FOR OPEN QUANTUM SYSTEMS WITHIN THE LINDBLAD THEORY." International Journal of Modern Physics B 10, no. 22 (October 10, 1996): 2767–79. http://dx.doi.org/10.1142/s0217979296001240.

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The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this function is given by a sum of three parts: the classical one, the quantum corrections and the contribution due to the opening of the system. In the particular case of a harmonic oscillator, quantum corrections do not exist.

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Malavazi, André Hernandes Alves, and Frederico Brito. "A Schmidt Decomposition Approach to Quantum Thermodynamics." Entropy 24, no. 11 (November 12, 2022): 1645. http://dx.doi.org/10.3390/e24111645.

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The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.

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Fickler, Robert, Geoff Campbell, Ben Buchler, Ping Koy Lam, and Anton Zeilinger. "Quantum entanglement of angular momentum states with quantum numbers up to 10,010." Proceedings of the National Academy of Sciences 113, no. 48 (November 15, 2016): 13642–47. http://dx.doi.org/10.1073/pnas.1616889113.

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Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM content per photon is known, they are also interesting systems to experimentally challenge quantum mechanical prediction for high quantum numbers. Here, we take advantage of a recently developed technique to imprint unprecedented high values of OAM, namely spiral phase mirrors, to generate photons with more than 10,000 quanta of OAM. Moreover, we demonstrate quantum entanglement between these large OAM quanta of one photon and the polarization of its partner photon. To our knowledge, this corresponds to entanglement with the largest quantum number that has been demonstrated in an experiment. The results may also open novel ways to couple single photons to massive objects, enhance angular resolution, and highlight OAM as a promising way to increase the information capacity of a single photon.

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RODRÍGUEZ-ROSARIO, CÉSAR A., and E. C. G. SUDARSHAN. "NON-MARKOVIAN OPEN QUANTUM SYSTEMS: SYSTEM–ENVIRONMENT CORRELATIONS IN DYNAMICAL MAPS." International Journal of Quantum Information 09, no. 07n08 (October 2011): 1617–34. http://dx.doi.org/10.1142/s0219749911008325.

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We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

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Sergi, Alessandro, Gabriel Hanna, Roberto Grimaudo, and Antonino Messina. "Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths." Symmetry 10, no. 10 (October 16, 2018): 518. http://dx.doi.org/10.3390/sym10100518.

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Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.

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Liu, Zhe, Alessandro Sergi, and Gabriel Hanna. "DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach." Applied Sciences 12, no. 14 (July 12, 2022): 7022. http://dx.doi.org/10.3390/app12147022.

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Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed.

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Han, Yongjian, Zhen Wang, and Guang-Can Guo. "A new epoch of quantum manipulation." National Science Review 1, no. 1 (December 24, 2013): 91–100. http://dx.doi.org/10.1093/nsr/nwt024.

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Abstract The behavior of individual microscopic particles, such as an atom (or a photon), predicted using quantum mechanics, is dramatically different from the behavior of classical particles, such as a planet, determined using classical mechanics. How can the counter-intuitive behavior of the microscopic particle be verified and manipulated experimentally? David Wineland and Serge Haroche, who were awarded the Nobel Prize in physics in 2012, developed a set of methods to isolate the ions and photons from their environment to create a genuine quantum system. Furthermore, they also developed methods to measure and manipulate these quantum systems, which open a path not only to explore the fundamental principles of quantum mechanics, but also to develop a much faster computer: a quantum computer.

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La Cour, Brian R. "Classical model of quantum interferometry tests of macrorealism." AVS Quantum Science 4, no. 4 (December 2022): 041402. http://dx.doi.org/10.1116/5.0131209.

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Macrorealism is a characteristic feature of many, but not all, classical systems. It is known, for example, that classical light can violate a Leggett–Garg inequality and, hence, reject a macrorealist interpretation. A recent experiment has used entangled light and negative measurements to demonstrate a loophole-free test of macrorealism [Joarder et al., PRX Quantum 3, 010307 (2022)]. This paper shows that such an experiment, while soundly rejecting macrorealism, may nevertheless be open to a classical interpretation. This is done by offering an explicit classical model of heralded photon detection in an optical interferometer with beam blockers. A numerical analysis of the model shows good agreement with experimental observations and consistency with both local realism and a rejection of macrorealism.

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Lippolis, Domenico, and Akira Shudo. "Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise." Entropy 25, no. 3 (February 24, 2023): 411. http://dx.doi.org/10.3390/e25030411.

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We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker–Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.

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FRANCO, ROSARIO LO, BRUNO BELLOMO, SABRINA MANISCALCO, and GIUSEPPE COMPAGNO. "DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS." International Journal of Modern Physics B 27, no. 01n03 (November 26, 2012): 1345053. http://dx.doi.org/10.1142/s0217979213450537.

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Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.

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Reiher, Markus, Nathan Wiebe, Krysta M. Svore, Dave Wecker, and Matthias Troyer. "Elucidating reaction mechanisms on quantum computers." Proceedings of the National Academy of Sciences 114, no. 29 (July 3, 2017): 7555–60. http://dx.doi.org/10.1073/pnas.1619152114.

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With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

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Carabba, Nicoletta, Niklas Hörnedal, and Adolfo del Campo. "Quantum speed limits on operator flows and correlation functions." Quantum 6 (December 22, 2022): 884. http://dx.doi.org/10.22331/q-2022-12-22-884.

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Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.

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Rocchetto, Andrea. "Stabiliser states are efficiently PAC-learnable." Quantum Information and Computation 18, no. 7&8 (June 2018): 541–52. http://dx.doi.org/10.26421/qic18.7-8-1.

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The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state tomography. State tomography, whose objective is to obtain an approximate description of a quantum system, can be analysed in the framework of computational learning theory. In this model, Aaronson (2007) showed that quantum states are Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits. However, it is conjectured that in general quantum states require an exponential amount of computation to be learned. Here, using results from the literature on the efficient classical simulation of quantum systems, we show that stabiliser states are efficiently PAC-learnable. Our results solve an open problem formulated by Aaronson (2007) and establish a connection between classical simulation of quantum systems and efficient learnability.

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Koruga, Ðuro. "DNA as classical and quantum information system: Implication to gene expression in normal and cancer cells." Archive of Oncology 13, no. 3-4 (2005): 115–20. http://dx.doi.org/10.2298/aoo0504115k.

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Usually, we think about DNA as a molecular machinery system responsible to make proteins. Protein looks like a second side of DNA code because mapping function is based on a classical information system (chemical/physical) by code 43=64. However, in organisms like paramecium DNA works 95% as molecular machinery for proteins synthesis, while in humans it is only about 10%. Is 90% of human genetic structure "junk"? What does other 90% DNA work in human organism? What type of information system, different than classical, does DNA possess? To give answer to this question we are rethinking well-known facts of biomolecules from both classical and quantum information point of view. Basic element in our consideration is hydrogen bond, which possess both classical and quantum properties. Based on new vision of old data we develop synergetic (classical/quantum) model of DNA information processing, which may help for better understanding the functions of "junk" sequence in genetic code. We believe that "junk" sequences may be active regulatory factor of system complexity trough microtubules (centrioles) and water in living systems. Synergetic approach (classical/quantum) of information channels may open a new vision and understanding of the genomic programming and molecular interconnection on distance based on matching classical and quantum properties of hydrogen bonds and entanglement. .

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Journal articles on the topic 'Open quantum systems, quantum-to-classical crossover'

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