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| Paper IPM / Physic / 13860 |
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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. In the final, we explain the evaluation of MIN for 3×n dimensional states in details.
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