Detection of the Entanglement in Many-Qubit Quantum Systems on the Basis of the Mermin and Ardehali Criteria
DOI:
https://doi.org/10.15407/ujpe61.12.1061Keywords:
quantum entanglement, entanglement criteriaAbstract
A possibility to reveal the entanglement in generalized n-qubit two-parameter GHZ states, as well as in any n-qubit states, with the help of the Mermin and Ardehali inequalities from the collection generally called the Mermin–Ardehali–Belinskii–Klyshko inequalities has been studied. Formulas for the calculation of the Mermin and Ardehali correlation functions in any quantum n-qubit states are derived, and criteria of the violation of corresponding inequalities by specific states are obtained. A set of states that are absolutely insensitive to the Mermin and Ardehali operators is revealed. Modified Mermin and Ardehali operators are proposed, the set of which makes it possible to extend the class of n-qubit states, in which quantum correlations can be revealed.
References
G. Gour, N.R. Wallach. The resource theory of quantum reference frames: Manipulations and monotones. New J. Phys. 13, 073013 (2011) https://doi.org/10.1088/1367-2630/10/3/033023
M. Walter, B. Doran, D. Gross, M. Christandl. Entanglement polytopes: Multiparticle entanglement from single-particle information. Science 340, 1205 (2013) https://doi.org/10.1126/science.1232957
W. D?ur, H.J. Briegel, J.I. Cirac, P. Zoller. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000) https://doi.org/10.1103/PhysRevA.62.062314
G. Gour, N.R. Wallach. All maximally entangled fourqubit states. J. Meth. Phys. (N.Y.) 51, 112201 (2010) https://doi.org/10.1063/1.3511477
G. Gour, N.R. Wallach. Classification of multipartite entanglement of all finite dimensionality. Phys. Rev. Lett. 111, 060502 (2013) https://doi.org/10.1103/PhysRevLett.111.060502
N. Gisin. Bell’s inequality holds for all non-product states. Phys. Lett. A 154, 201 (1991) https://doi.org/10.1016/0375-9601(91)90805-I
N. Gisin, A. Peres. Maximal violation of Bell’s inequality for arbitrarily large spin. Phys. Lett. A 162, 15 (1992) https://doi.org/10.1016/0375-9601(92)90949-M
J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969) https://doi.org/10.1103/PhysRevLett.23.880
Jing-Ling Chen, Chunfeng Wu, L.C. Kwek, C.H. Oh. Gisin’s theorem for three qubits. Phys. Rev. Lett. 93, 140407 (2004) https://doi.org/10.1103/PhysRevLett.93.140407
N.D. Mermin. Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838 (1990) https://doi.org/10.1103/PhysRevLett.65.1838
M. Ardehali. Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Phys. Rev. A 46, 5375 (1992) https://doi.org/10.1103/PhysRevA.46.5375
A.V. Belinskii, D.N. Klyshko. Interference of light and Bell’s theorem. Phys. Usp. 36, 653 (1993) https://doi.org/10.1070/PU1993v036n08ABEH002299
D.M. Greenberger, M. Horne, A. Shimony, A. Zeilenger. Bell’s theorem without inequalities. Am. J. Phys. 58, 1131 (1990) https://doi.org/10.1119/1.16243
V. Scarani, N. Gisin. Spectral decomposition of Bell’s operators for qubits. J. Phys. A 34 6043 (2011) https://doi.org/10.1088/0305-4470/34/30/314
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