Measurement-induced nonlocality for an arbitrary bipartite state
Measurement-induced nonlocality for an arbitrary bipartite state
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DOI：
10.26421/qic13.5-6-8
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发表时间：
2011-10
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影响因子：
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通讯作者：
S. Y. Mirafzali;Iman Sargolzahi;A. Ahanj;K. Javidan;M. Sarbishaei
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文献类型：
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作者：
S. Y. Mirafzali;Iman Sargolzahi;A. Ahanj;K. Javidan;M. Sarbishaei
测量诱导非局域性是由Luo和Fu[物理学]提出的一种非局域性测度。科学通报，2012,(1)[j]。本文研究了任意m × n维二部密度矩阵ρ在其中一个约简密度矩阵ρ是简并的情况下的测量诱导非定域性（MIN）的评价问题（非简并的情况在前面的参考文献中有解释）。一般情况下，ρa有d个维数为mi（mi≤m, i = 1,2，…）的简并子空间d)。我们证明了根据ρ的简并性，如果我们在合适的基中展开ρ，则m × n维状态ρ的MIN的求值，可以退化为在状态ρ的mi × n维子空间中求MIN。该方法可以减少最小值评估中的计算量。此外，对于mi≤2的任意m × n状态ρ，我们的方法可以得到精确的MIN值。此外，我们还得到了最小值的一个上界，它可以改进上述文献中所介绍的上界。最后，我们详细解释了3 × n维状态下最小值的计算。
Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett 106, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary m × n dimensional bipartite density matrix ρ for the case where one of its reduced density matrix, ρa, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general, ρa has d degenerate subspaces with dimension mi(mi ≤ m, i = 1, 2, ..., d). We show that according to the degeneracy of ρa, if we expand ρ in a suitable basis, the evaluation of MIN for an m × n dimensional state ρ, is degraded to finding the MIN in the mi × n dimensional subspaces of state ρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary m × n state ρ for which mi ≤ 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 × n dimensional states in details.