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Количественное выражение нелокальности Белла много-кудитного квантового состояния

2018

Nonlocality of an N-qudit quantum state, in the sense of its violation of a Bell inequality, is now used in many quantum information processing tasks, also, for nonlocal games strategies in computer science. Though entanglement is necessary for Bell nonlocality of an N-qudit state, it is not sufficient and there exist fully entangled N-qudit states that are fully Bell local. Moreover, since large violation of a Bell inequality by an N-qudit quantum state – implying its high Bell nonlocality -- can be attained by an entangled state with low entanglement, for quantifying of, for example, two-qudit quantum nonlocality, the entropy of entanglement is essentially irrelevant.      

In recent years, Bell nonlocality of a two-qudit (N=2, d≥2) quantum state was intensively studied in the literature and several measures were proposed for quantifying Bell nonlocality in a two-qudit quantum case. However, for N>2, even nonlocality of a multi-qubit (N>2, d=2) quantum state is not yet completely studied and quantified, so that the theory for multi-qudit quantum nonlocality (as well as the theory for multi-qudit quantum entanglement) is now still in infancy. However, study of multi-qudit quantum nonlocality is specifically important for security of quantum cryptography and quantum communication protocols. Furthermore, in quantum information applications, one deals with noisy channels and, for a nonlocal multi-qudit state, it is important to know amounts of noise breaking the non-classical character of its statistical correlations. However, the critical noise threshold for full Bell locality of a nonlocal N-qudit state mixed with white noise and, more generally, the resistance of a nonlocal N-qudit state to a noise of any type have been also analyzed only in a two-qudit case. In the proposed research, I intend to study a wide range of open problems on quantifying Bell nonlocality of multi-qudit quantum correlations, in particular: (a) to find a general analytical criterion for Bell nonlocality of a multipartite quantum state expressed in terms of Hilbert space characteristics of this state; (b) to quantify Bell nonlocality of a multi-qudit quantum state via its maximal violation of general Bell inequalities, also, via its resistance to noise; (c) to compare the general properties of the introduced new multi-qudit nonlocality measures and to specify their values for the multi-qudit states used in quantum information applications, namely, for the multi-qudit GHZ state, the multi-qudit Dicke class states, the multi-qudit W states; (d) to find the critical noise thresholds for full Bell locality of an arbitrary nonlocal multi-qudit state and some specific multi-qudit states (see above) mixed with white noise; (e) to analyze the application of the projected results in quantum cryptography and quantum communication.     The projected results are planned to be published in the leading foreign journals on quantum information and to be reported at the main conferences/ workshops on this subject.  

Публикации по проекту:


Elena R. Loubenets, Andrei Y. K. Quantum analog of the original Bell inequality for two-qudit states with perfect correlations/anticorrelations // Journal of Physics A: Mathematical and Theoretical. 2019. Vol. 52. No. 43. P. 435304-1-435304-14. doi