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中国物理B：英文版

Measurement-induced nonlocality in the W and Greenberger–Horne–Zeilinger superposition states

林秦, 白彦魁, 叶明勇, 林秀敏

Published Jan 1, 2015• 0 citations
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Abstract

Measurement-induced nonlocality(MIN) is a newly defined quantity to measure correlations in bipartite quantum states [Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401]. MIN in the n-qubit W and Greenberger–Horne–Zeilinger(GHZ) superposition states is considered. It is revealed that n = 3 and n ≥ 4 states have very different characteristics,especially the monogamy relation about MIN, and the monogamy equality of MIN is held in all n-qubit W states(n ≥ 3).更多还原

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Measurement-induced nonlocality(MIN) is a newly defined quantity to measure correlations in bipartite quantum states [Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401]. MIN in the n-qubit W and Greenberger–Horne–Zeilinger(GHZ) superposition states is considered. It is revealed that n = 3 and n ≥ 4 states have very different characteristics,especially the monogamy relation about MIN, and the monogamy equality of MIN is held in all n-qubit W states(n ≥ 3).更多还原
Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.
Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary m×nm\times nm×n dimensional bipartite density matrix ρρρ for the case where one of its reduced density matrix, ρaρ^{a}ρa, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general, ρaρ^{a}ρa has ddd degenerate subspaces with dimension mi(mi≤m,i=1,2,...,d)m_{i} (m_{i} \leq m, i=1, 2, ..., d)mi​(mi​≤m,i=1,2,...,d). We show that according to the degeneracy of ρaρ^{a}ρa, if we expand ρρρ in a suitable basis, the evaluation of MIN for an m×nm\times nm×n dimensional state ρρρ, is degraded to finding the MIN in the mi×nm_{i}\times nmi​×n dimensional subspaces of state ρρρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary m×nm\times nm×n state ρρρ for which mi≤2m_{i}\leq 2mi​≤2, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. In the final, we explain the evaluation of MIN for 3×n3\times n3×n dimensional states in details.
Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary m×nm\times nm×n dimensional bipartite density matrix ρ\rhoρ for the case where one of its reduced density matrix, ρa\rho^{a}ρa, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general, ρa\rho^{a}ρa has ddd degenerate subspaces with dimension mi(mi≤m,i=1,2,...,d)m_{i} (m_{i} \leq m , i=1, 2, ..., d)mi​(mi​≤m,i=1,2,...,d). We show that according to the degeneracy of ρa\rho^{a}ρa, if we expand ρ\rhoρ in a suitable basis, the evaluation of MIN for an m×nm\times nm×n dimensional state ρ\rhoρ, is degraded to finding the MIN in the mi×nm_{i}\times nmi​×n dimensional subspaces of state ρ\rhoρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary m×nm\times nm×n state ρ\rhoρ for which mi≤2m_{i}\leq 2mi​≤2, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. Finally, we explain the evaluation of MIN for 3×n3\times n3×n dimensional states in details.
Measurement-induced nonlocality (MIN), introduced by Luo and Fu [Phys. Rev. Lett.106, 120401 (2011)], is a kind of quantum correlation which is different from entanglement and quantum discord (QD). MIN is defined over one-sided projective measurements. In this paper, we introduce a MIN over two-sided projective measurements. The nullity of this two-sided MIN is characterized, a formula for calculating two-sided MIN for pure states is proposed, and a lower bound of (two-sided) MIN for maximally entangled mixed states is given. In addition, we find that (two-sided) MIN is not continuous. Both finite- and infinite-dimensional cases are considered.
Measurement-induced nonlocality (MIN), which describes the maximum global effect caused by locally invariant measurements, was introduced by Luo and Fu ( Phys. Rev. Lett. , 106 (2011) 120401). In this paper, a new measure of MIN based on Wigner-Yanase skew information is proposed. It is shown that this measure not only has good computability but also eliminates the noncontractivity problem appearing in the original measure of MIN defined by the Hilbert-Schmidt norm. The analytical formulas of MIN based on Wigner-Yanase skew information for any pure states, ( 2 × n ) -dimensional mixed states, and some higher-dimensional symmetric states are presented. Furthermore, the tight upper bound to MIN based on Wigner-Yanase skew information in the general case is also derived.