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Статті в журналах з теми "Entanglement Classification"

Автор: Grafiati

Опубліковано: 11 березня 2023

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1

Sanz, M., D. Braak, E. Solano, and I. L. Egusquiza. "Entanglement classification with algebraic geometry." Journal of Physics A: Mathematical and Theoretical 50, no. 19 (April 18, 2017): 195303. http://dx.doi.org/10.1088/1751-8121/aa6926.

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2

Chitambar, Eric, Carl A. Miller, and Yaoyun Shi. "Matrix pencils and entanglement classification." Journal of Mathematical Physics 51, no. 7 (July 2010): 072205. http://dx.doi.org/10.1063/1.3459069.

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3

Wang, Pingxun. "A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification." Applied Sciences 12, no. 24 (December 13, 2022): 12778. http://dx.doi.org/10.3390/app122412778.

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Анотація:

Quantum entanglement becomes more complicated and capricious when more than two parties are involved. There have been methods for classifying some inequivalent multipartite entanglements, such as GHZ states and W states. In this paper, based on the fact that the set of all W states is convex, we approximate the convex hull by some critical points from the inside and propose a method of classification via the tangent hyperplane. To accelerate the calculation, we bring ensemble learning of machine learning into the algorithm, thus improving the accuracy of the classification.

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4

AULBACH, MARTIN. "CLASSIFICATION OF ENTANGLEMENT IN SYMMETRIC STATES." International Journal of Quantum Information 10, no. 07 (October 2012): 1230004. http://dx.doi.org/10.1142/s0219749912300045.

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Анотація:

Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis, the entanglement of symmetric multipartite states is categorized, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalization of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n-qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterization of entanglement equivalence classes such as stochastic local operations and classical communication (SLOCC) and the degeneracy configuration (DC). It is found that SLOCC operations between symmetric states can be described by the Möbius transformations of complex analysis, which allows for a clear visualization of the SLOCC freedoms and facilitates the understanding of SLOCC invariants and equivalence classes. In particular, explicit forms of representative states for all symmetric SLOCC classes of up to five qubits are derived. Well-known entanglement classification schemes such as the four qubit entanglement families or polynomial invariants are reviewed in the light of the results gathered here, which leads to sometimes surprising connections. Some interesting links and applications of the Majorana representation to related fields of mathematics and physics are also discussed.

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5

Jafarizadeh, M. A., F. Eghbalifam, S. Nami, and M. Yahyavi. "Entanglement classification in the noninteracting Fermi gas." International Journal of Quantum Information 15, no. 07 (October 2017): 1750055. http://dx.doi.org/10.1142/s0219749917500551.

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In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group [Formula: see text]. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur–Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even [Formula: see text] qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of [Formula: see text]. The restricted density matrix to the subspaces of the irreducible representations: [Formula: see text], [Formula: see text] and [Formula: see text] are denoted by [Formula: see text], [Formula: see text] and [Formula: see text], respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix [Formula: see text] and [Formula: see text], so these classes do not exist in the total Fermi gas density matrix.

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6

CHEN, LIN, and MASAHITO HAYASHI. "NONDISTILLABLE ENTANGLEMENT GUARANTEES DISTILLABLE ENTANGLEMENT." International Journal of Modern Physics B 26, no. 27n28 (September 18, 2012): 1243008. http://dx.doi.org/10.1142/s0217979212430084.

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The monogamy of entanglement is one of the basic quantum mechanical features, which says that when two partners Alice and Bob are more entangled then either of them has to be less entangled with the third party. Here we qualitatively present the converse monogamy of entanglement: given a tripartite pure system and when Alice and Bob are entangled and nondistillable, then either of them is distillable with the third party. Our result leads to the classification of tripartite pure states based on bipartite reduced density operators, which is a novel and effective way to this long-standing problem compared to the means by stochastic local operations and classical communications. Furthermore we systematically indicate the structure of the classified states and generate them. We also extend our results to multipartite states.

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7

Lyons, David W., Abigail M. Skelton, and Scott N. Walck. "Werner State Structure and Entanglement Classification." Advances in Mathematical Physics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/463610.

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We present applications of the representation theory of Lie groups to the analysis of structure and local unitary classification of Werner states, sometimes called thedecoherence-freestates, which are states ofnquantum bits left unchanged by local transformations that are the same on each particle. We introduce a multiqubit generalization of the singlet state and a construction that assembles these qubits into Werner states.

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8

Fu, Hongchen, Xiaoguang Wang, and Allan I. Solomon. "Maximal entanglement of nonorthogonal states: classification." Physics Letters A 291, no. 2-3 (December 2001): 73–76. http://dx.doi.org/10.1016/s0375-9601(01)00720-4.

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9

Chruściński, Dariusz, and Gniewomir Sarbicki. "Entanglement witnesses: construction, analysis and classification." Journal of Physics A: Mathematical and Theoretical 47, no. 48 (November 11, 2014): 483001. http://dx.doi.org/10.1088/1751-8113/47/48/483001.

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10

Zhao, Hui, Yu-Qiu Liu, Zhi-Xi Wang, and Shao-Ming Fei. "A note on entanglement classification for tripartite mixed states." Acta Polytechnica 62, no. 1 (February 28, 2022): 222–27. http://dx.doi.org/10.14311/ap.2022.62.0222.

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Анотація:

We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell inequalities which classifies the entanglement of triqutrit fully separable and bi-separable mixed states. By using the correlation tensors in the principal basis representation of density matrices, we obtain separability criteria for fully separable and bi-separable 2 ⊗ 2 ⊗ 3 quantum mixed states. Detailed example is given to illustrate our criteria in classifying the tripartite entanglement.

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11

BARTLETT, STEPHEN D., HOWARD M. WISEMAN, ROBERT W. SPEKKENS, and ANDREW C. DOHERTY. "MIXED-STATE ENTANGLEMENT IN THE LIGHT OF PURE-STATE ENTANGLEMENT CONSTRAINED BY SUPERSELECTION RULES." International Journal of Quantum Information 03, supp01 (November 2005): 145–53. http://dx.doi.org/10.1142/s021974990500133x.

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We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

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12

Mengoni, Ricardo, Alessandra Di Pierro, Leleh Memarzadeh, and Stefano Mancini. "Persistent homology analysis of multiqubit entanglement." Quantum Information and Computation 20, no. 5&6 (May 2020): 375–99. http://dx.doi.org/10.26421/qic20.5-6-2.

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We introduce a homology-based technique for the classification of multiqubit state vectors with genuine entanglement. In our approach, we associate state vectors to data sets by introducing a metric-like measure in terms of bipartite entanglement, and investigate the persistence of homologies at different scales. This leads to a novel classification of multiqubit entanglement. The relative occurrence frequency of various classes of entangled states is also shown.

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13

PAN, FENG, GUOYING LU, and J. P. DRAAYER. "CLASSIFICATION AND QUANTIFICATION OF ENTANGLED BIPARTITE QUTRIT PURE STATES." International Journal of Modern Physics B 20, no. 11n13 (May 20, 2006): 1333–42. http://dx.doi.org/10.1142/s0217979206033966.

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Анотація:

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

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14

Rizvi, Syed Muhammad Abuzar, Naema Asif, Muhammad Shohibul Ulum, Trung Q. Duong, and Hyundong Shin. "Multiclass Classification of Metrologically Resourceful Tripartite Quantum States with Deep Neural Networks." Sensors 22, no. 18 (September 7, 2022): 6767. http://dx.doi.org/10.3390/s22186767.

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Анотація:

Quantum entanglement is a unique phenomenon of quantum mechanics, which has no classical counterpart and gives quantum systems their advantage in computing, communication, sensing, and metrology. In quantum sensing and metrology, utilizing an entangled probe state enhances the achievable precision more than its classical counterpart. Noise in the probe state preparation step can cause the system to output unentangled states, which might not be resourceful. Hence, an effective method for the detection and classification of tripartite entanglement is required at that step. However, current mathematical methods cannot robustly classify multiclass entanglement in tripartite quantum systems, especially in the case of mixed states. In this paper, we explore the utility of artificial neural networks for classifying the entanglement of tripartite quantum states into fully separable, biseparable, and fully entangled states. We employed Bell’s inequality for the dataset of tripartite quantum states and train the deep neural network for multiclass classification. This entanglement classification method is computationally efficient due to using a small number of measurements. At the same time, it also maintains generalization by covering a large Hilbert space of tripartite quantum states.

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15

Evans, Myfanwy E., and Stephen T. Hyde. "Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests." Acta Crystallographica Section A Foundations and Advances 71, no. 6 (October 20, 2015): 599–611. http://dx.doi.org/10.1107/s2053273315014710.

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Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane ({\bb H}^2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in {\bb H}^2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal–organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given inPeriodic entanglementParts I and II [Evanset al.(2013).Acta Cryst.A69, 241–261; Evanset al.(2013).Acta Cryst.A69, 262–275].

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16

Li, Yan, and Zhihong Ren. "Nonlocal operation enhanced entanglement detection and classification." Physica A: Statistical Mechanics and its Applications 596 (June 2022): 127137. http://dx.doi.org/10.1016/j.physa.2022.127137.

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17

Harney, Cillian, Stefano Pirandola, Alessandro Ferraro, and Mauro Paternostro. "Entanglement classification via neural network quantum states." New Journal of Physics 22, no. 4 (April 3, 2020): 045001. http://dx.doi.org/10.1088/1367-2630/ab783d.

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18

Seveso, Luigi, Dardo Goyeneche, and Karol Życzkowski. "Coarse-grained entanglement classification through orthogonal arrays." Journal of Mathematical Physics 59, no. 7 (July 2018): 072203. http://dx.doi.org/10.1063/1.5006890.

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19

Luna-Hernández, S. "Global and Bipartite Entanglement for Three-Qubit System Local Unitary Classes." Journal of Physics: Conference Series 2448, no. 1 (February 1, 2023): 012020. http://dx.doi.org/10.1088/1742-6596/2448/1/012020.

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Abstract Entanglement of multipartite quantum systems is an important resource in the field of quantum information processing. Using a measure of global entanglement and the notion of concurrence, the properties of entanglement for a three-qubit system are studied and classified in terms of local unitary classes. The connection of such classification with the three-qubit entanglement polytope is also discussed.

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20

Li, D. F., X. R. Li, H. T. Huang, and X. X. Li. "SLOCC classification for nine families of four-qubits." Quantum Information and Computation 9, no. 9&10 (September 2009): 778–800. http://dx.doi.org/10.26421/qic9.9-10-5.

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In 2000, D\"{u}r, Vidal and Cirac indicated that there are infinitely many SLOCC classes for four qubits. Later, Verstraete, Dehaene, and Verschelde proposed nine families of states corresponding to nine different ways of entangling four qubits. And then in 2007 Lamata et al. reported that there are eight true SLOCC entanglement classes of four qubits up to permutations of the qubits. In this paper, we investigate SLOCC classification of the nine families proposed by Verstraete, Dehaene and Verschelde, and distinguish 49 true SLOCC entanglement classes from them.

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21

Yang, F., G. Q. Zhou, J. R. Xiao, Q. Li, B. Jia, H. Y. Wang, and J. Gao. "MULTISPECTRAL REMOTE SENSING IMAGE CLASSIFICATION BASED ON QUANTUM ENTANGLEMENT." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W10 (February 7, 2020): 667–70. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w10-667-2020.

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Abstract. Aiming at the problems of low accuracy and slow speed in the current remote sensing image classification algorithm,In order to improve remote sensing image classification, a quantum entanglement algorithm is proposed.The model transforms the classification process of remote sensing image into a random self-organization process of quantum particles in the state configuration space. The state configuration formed by entanglement of quantum particles evolves with time and finally converges to an average probability distribution.Taking Kunming city of Yunnan province as the research area, this paper compares the classification method in this paper with the traditional remote sensing classification method by using the 02C image data of yuanyuan1.Compared with other classification methods, the classification accuracy of this paper meets the requirements.

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22

USHA DEVI, A. R., M. S. UMA, R. PRABHU, and SUDHA. "LOCAL INVARIANTS AND PAIRWISE ENTANGLEMENT IN SYMMETRIC MULTIQUBIT SYSTEM." International Journal of Modern Physics B 20, no. 11n13 (May 20, 2006): 1917–33. http://dx.doi.org/10.1142/s0217979206034406.

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Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett.95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.

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23

Akhound, Ahmad, Saeed Haddadi, and Mohammad Ali Chaman Motlagh. "Analyzing the entanglement properties of graph states with generalized concurrence." Modern Physics Letters B 33, no. 10 (April 10, 2019): 1950118. http://dx.doi.org/10.1142/s0217984919501185.

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We propose a new classification for the entanglement in graph states based on generalized concurrence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states in 10 classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule. Furthermore, our results suggest that the generalized concurrence is a suitable measure of entanglement for multi-qubit graph states.

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24

Harney, Cillian, Mauro Paternostro, and Stefano Pirandola. "Mixed state entanglement classification using artificial neural networks." New Journal of Physics 23, no. 6 (June 1, 2021): 063033. http://dx.doi.org/10.1088/1367-2630/ac0388.

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25

Sabín, C., and G. García-Alcaine. "A classification of entanglement in three-qubit systems." European Physical Journal D 48, no. 3 (June 6, 2008): 435–42. http://dx.doi.org/10.1140/epjd/e2008-00112-5.

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26

Abdel-Aty, Abdel-Haleem, Heba Kadry, Mohammed Zidan, Yazeed Al-Sbou, E. A. Zanaty, and Mahmoud Abdel-Aty. "A quantum classification algorithm for classification incomplete patterns based on entanglement measure." Journal of Intelligent & Fuzzy Systems 38, no. 3 (March 4, 2020): 2809–16. http://dx.doi.org/10.3233/jifs-179566.

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27

Merkli, M., G. P. Berman, F. Borgonovi, and K. Gebresellasie. "Evolution of entanglement." Quantum Information and Computation 11, no. 5&6 (May 2011): 390–419. http://dx.doi.org/10.26421/qic11.5-6-3.

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Анотація:

We analyze the dynamics of entanglement between two qubits which interact through collective and local environments. Our approach is based on a resonance theory which assumes a small interaction between qubits and environments and which gives rigorous perturbation theory results, valid for all times. We obtain expressions for (i) characteristic time-scales for decoherence, relaxation, disentanglement, and for (ii) the evolution of observables, valid uniformly in time $t\geq 0$. We introduce a classification of decoherence times based on clustering of the reduced density matrix elements, persisting on all time-scales. We examine characteristic dynamical properties such as creation, death and revival of entanglement. We discuss possible applications of our results for superconducting quantum computation and quantum measurement technologies.

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28

Jung, Eylee, and DaeKil Park. "Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states." Quantum Information and Computation 14, no. 11&12 (September 2014): 937–48. http://dx.doi.org/10.26421/qic14.11-12-3.

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In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

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29

Kienitz, Daniel, Ekaterina Komendantskaya, and Michael Lones. "The Effect of Manifold Entanglement and Intrinsic Dimensionality on Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (June 28, 2022): 7160–67. http://dx.doi.org/10.1609/aaai.v36i7.20676.

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We empirically investigate the effect of class manifold entanglement and the intrinsic and extrinsic dimensionality of the data distribution on the sample complexity of supervised classification with deep ReLU networks. We separate the effect of entanglement and intrinsic dimensionality and show statistically for artificial and real-world image datasets that the intrinsic dimensionality and the entanglement have an interdependent effect on the sample complexity. Low levels of entanglement lead to low increases of the sample complexity when the intrinsic dimensionality is increased, while for high levels of entanglement the impact of the intrinsic dimensionality increases as well. Further, we show that in general the sample complexity is primarily due to the entanglement and only secondarily due to the intrinsic dimensionality of the data distribution.

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30

Anticoli, Linda, and Masoud Gharahi Ghahi. "Modeling tripartite entanglement in quantum protocols using evolving entangled hypergraphs." International Journal of Quantum Information 16, no. 07 (October 2018): 1850055. http://dx.doi.org/10.1142/s0219749918500557.

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Анотація:

The notion of entanglement is the most well-known nonclassical correlation in quantum mechanics, and a fundamental resource in quantum information and computation. This correlation, which is displayed by certain classes of quantum states, is of utmost importance when dealing with protocols, such as quantum teleportation, cryptography and quantum key distribution. In this paper, we exploit a classification of tripartite entanglement by introducing the concepts of entangled hypergraph and evolving entangled hypergraph as data structures suitable to model quantum protocols which use entanglement. Finally, we present a few examples to provide applications of this model.

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31

Zangi, S. M., Jun-Li Li, and Cong-Feng Qiao. "Entanglement classification of four-partite states under the SLOCC." Journal of Physics A: Mathematical and Theoretical 50, no. 32 (July 14, 2017): 325301. http://dx.doi.org/10.1088/1751-8121/aa7a2d.

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32

Xin-Gang, Yang, Wang Zhi-Xi, Wang Xiao-Hong, and Fei Shao-Ming. "Classification of Bipartite and Tripartite Qutrit Entanglement Under SLOCC." Communications in Theoretical Physics 50, no. 3 (September 2008): 651–54. http://dx.doi.org/10.1088/0253-6102/50/3/25.

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33

Li, Xiangrong, and Dafa Li. "Rank-based SLOCC classification for odd $n$ qubits." Quantum Information and Computation 11, no. 7&8 (July 2011): 695–705. http://dx.doi.org/10.26421/qic11.7-8-10.

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Анотація:

We study the entanglement classification under stochastic local operations and classical communication (SLOCC) for odd n-qubit pure states. For this purpose, we introduce the rank with respect to qubit i for an odd n-qubit state. The ranks with respect to qubits 1,2, ... n give rise to the classification of the space of odd $n$ qubits into 3^n families.

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34

Miyake, A., and M. Wadati. "Multipartite entanglement and hyperdeterminants." Quantum Information and Computation 2, Special (November 2002): 540–55. http://dx.doi.org/10.26421/qic2.s-4.

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We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical \(n\)-partite entangled states. Our classification is also useful for that of mixed states.

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35

Hsu, Li-Yi, and Shoichi Kawamoto. "Exploring Multipartite Steering Effect Using Bell Operators." Entropy 22, no. 1 (December 23, 2019): 19. http://dx.doi.org/10.3390/e22010019.

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While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

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36

Conix, Stijn. "Enzyme classification and the entanglement of values and epistemic standards." Studies in History and Philosophy of Science Part A 84 (December 2020): 37–45. http://dx.doi.org/10.1016/j.shpsa.2020.05.005.

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37

Assadi, Leila, and Mojtaba Jafarpour. "Classification of 4-qubit Entangled Graph States According to Bipartite Entanglement, Multipartite Entanglement and Non-local Properties." International Journal of Theoretical Physics 55, no. 11 (July 12, 2016): 4809–21. http://dx.doi.org/10.1007/s10773-016-3104-x.

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38

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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39

Bennett, C. H. "A resource-based view of quantum information." Quantum Information and Computation 4, no. 6&7 (December 2004): 460–66. http://dx.doi.org/10.26421/qic4.6-7-5.

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We survey progress in understanding quantum information in terms of equivalences, reducibilities, and asymptotically achievable rates for transformations among nonlocal resources such as classical communication, entanglement, and particular quantum states or channels. In some areas, eg source coding, there are straightforward parallels to classical information theory; in others eg entanglement-assisted communication, new effects and tradeoffs appear that are beginning to be fairly well understood, or the remaining uncertainty has become focussed on a few simple open questions, such as conjectured additivity of the Holevo capacity. In still other areas, e.g. the role of the back communication and the classification of tripartite entanglement, much remains unknown, and it appears unlikely that an adequate description exists in terms of a finite number of resources.

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40

Jacak, Janusz. "Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields." Materials 14, no. 7 (March 27, 2021): 1650. http://dx.doi.org/10.3390/ma14071650.

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Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

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41

ASHOURISHEIKHI, SAKINEH, and SWARNAMALA SIRSI. "LOCAL UNITARY EQUIVALENT CLASSES OF SYMMETRIC N-QUBIT MIXED STATES." International Journal of Quantum Information 11, no. 08 (December 2013): 1350072. http://dx.doi.org/10.1142/s021974991350072x.

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Majorana representation (MR) of symmetric N-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the difficulties faced in the construction of a Majorana like geometric representation for symmetric mixed state. We have overcome this problem by developing a method of classifying local unitary (LU) equivalent classes of symmetric N-qubit mixed states based on the geometrical multiaxial representation (MAR) of the density matrix. In addition to the two parameters defined for the entanglement classification of the symmetric pure states based on MR, namely, diversity degree and degeneracy configuration, we show that another parameter called rank needs to be introduced for symmetric mixed state classification. Our scheme of classification is more general as it can be applied to both pure and mixed states. To bring out the similarities/differences between the MR and MAR, N-qubit GHZ state is taken up for a detailed study. We conclude that pure state classification based on MR is not a special case of our classification scheme based on MAR. We also give a recipe to identify the most general symmetric N-qubit pure separable states. The power of our method is demonstrated using several well-known examples of symmetric two-qubit pure and mixed states as well as three-qubit pure states. Classification of uniaxial, biaxial and triaxial symmetric two-qubit mixed states which can be produced in the laboratory is studied in detail.

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42

Borsten, L. "The Freudenthal triple classification of 3-qubit entanglement andSTUblack hole entropy." Journal of Physics: Conference Series 462 (December 31, 2013): 012005. http://dx.doi.org/10.1088/1742-6596/462/1/012005.

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43

Lu Guo-Ying and Pan Feng. "Classification and quantification of qubit and qutrit multipartite pure state entanglement." Acta Physica Sinica 56, no. 4 (2007): 1895. http://dx.doi.org/10.7498/aps.56.1895.

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44

Cao, Y., and A. M. Wang. "Discussion of the entanglement classification of a 4-qubit pure state." European Physical Journal D 44, no. 1 (May 4, 2007): 159–66. http://dx.doi.org/10.1140/epjd/e2007-00148-y.

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45

Osterloh, A. "Classification of qubit entanglement: SL(2,ℂ) versus SU(2) invariance". Applied Physics B 98, № 4 (7 січня 2010): 609–16. http://dx.doi.org/10.1007/s00340-009-3859-3.

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46

Meshi, Avital, and Angus G. Forbes. "Stepping Inside the Classification Cube: An Intimate Interaction with an AI System." Leonardo 53, no. 4 (July 2020): 387–93. http://dx.doi.org/10.1162/leon_a_01924.

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The Classification Cube art installation invites participants to become familiar with a machine-learning classification system. Inside a private space within the gallery, participants’ bodies are subjected to a classification process that detects their faces and estimates their age, gender, emotion and actions. Participants are also able to see how their own classification compares with how the installation classifies a series of animated figures. Rapidly changing results encourage participants to actively perform their behavior to the system and alter the way it “sees” them. The entanglement with the system raises awareness regarding the effectiveness of machine interpretation.

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47

Wang, Zhi Guo. "Preparation and Measurement of Quantum State between Two-Dimensional Dots in Quantum Network." Applied Mechanics and Materials 543-547 (March 2014): 2742–45. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2742.

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Currently, researches on the preparation and measurement of quantum state between two-dimensional dots in quantum network are mainly dot-to-dot or dot-to-multi-dot transmission schemes. The existing experimental and theoretical work is relatively scattered, and the overall knowledge is incomplete. The article proposes the preparation of multiple quantum entanglement state, the measurement and classification of multi-state and multi-body quantum entanglement, the design of the preparation and measurement scheme of quantum state between any two one-dimensional dots and proposes the transmission scheme of quantum state between two-dimensional dots in quantum network. Theoretical guidance is provided for relevant experiments through deep study on the problem.

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48

Ralston, John P. "What Can We Learn from Entanglement and Quantum Tomography?" Physics 4, no. 4 (November 12, 2022): 1371–83. http://dx.doi.org/10.3390/physics4040088.

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Entanglement has become a hot topic in nuclear and particle physics, although many physicists are not sure they know what it means. We maintain that an era of understanding and using quantum mechanics on a dramatically new basis has arrived. We review a viewpoint that treats the subject as being primarily descriptive and completely free of the intellectual straitjackets and mysticism argued over long ago. Quantum probability is an extension of classical probability, but with universal uses. Density matrices describe systems where entanglement or its absence is a classification tool. Most of these have been known for decades, but there is a new way of understanding them that is liberated from the narrow outlook of the early days.

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49

Zidan, Mohammed, Abdel-Haleem Abdel-Aty, Mahmoud El-shafei, Marwa Feraig, Yazeed Al-Sbou, Hichem Eleuch, and Mahmoud Abdel-Aty. "Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure." Applied Sciences 9, no. 7 (March 27, 2019): 1277. http://dx.doi.org/10.3390/app9071277.

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In this paper, we develop a novel classification algorithm that is based on the integration between competitive learning and the computational power of quantum computing. The proposed algorithm classifies an input into one of two binary classes even if the input pattern is incomplete. We use the entanglement measure after applying unitary operators to conduct the competition between neurons in order to find the winning class based on wining-take-all. The novelty of the proposed algorithm is shown in its application to the quantum computer. Our idea is validated via classifying the state of Reactor Coolant Pump of a Risky Nuclear Power Plant and compared with other quantum-based competitive neural networks model.

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50

Riaz, Farina, Shahab Abdulla, Hajime Suzuki, Srinjoy Ganguly, Ravinesh C. Deo, and Susan Hopkins. "Accurate Image Multi-Class Classification Neural Network Model with Quantum Entanglement Approach." Sensors 23, no. 5 (March 2, 2023): 2753. http://dx.doi.org/10.3390/s23052753.

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Quantum machine learning (QML) has attracted significant research attention over the last decade. Multiple models have been developed to demonstrate the practical applications of the quantum properties. In this study, we first demonstrate that the previously proposed quanvolutional neural network (QuanvNN) using a randomly generated quantum circuit improves the image classification accuracy of a fully connected neural network against the Modified National Institute of Standards and Technology (MNIST) dataset and the Canadian Institute for Advanced Research 10 class (CIFAR-10) dataset from 92.0% to 93.0% and from 30.5% to 34.9%, respectively. We then propose a new model referred to as a Neural Network with Quantum Entanglement (NNQE) using a strongly entangled quantum circuit combined with Hadamard gates. The new model further improves the image classification accuracy of MNIST and CIFAR-10 to 93.8% and 36.0%, respectively. Unlike other QML methods, the proposed method does not require optimization of the parameters inside the quantum circuits; hence, it requires only limited use of the quantum circuit. Given the small number of qubits and relatively shallow depth of the proposed quantum circuit, the proposed method is well suited for implementation in noisy intermediate-scale quantum computers. While promising results were obtained by the proposed method when applied to the MNIST and CIFAR-10 datasets, a test against a more complicated German Traffic Sign Recognition Benchmark (GTSRB) dataset degraded the image classification accuracy from 82.2% to 73.4%. The exact causes of the performance improvement and degradation are currently an open question, prompting further research on the understanding and design of suitable quantum circuits for image classification neural networks for colored and complex data.

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