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.
We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.
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.
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×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.
The original definition of quantum discord of bipartite states was defined under one-side projective measurements, it describes quantum correlation more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. \textbf{105}, 190502 (2010)] introduced a geometric measure of quantum discord, and Luo, Fu [Phys. Rev. A \textbf{82}, 034302 (2010)] simplified the expression of it. In this paper we generalize the quantum discord to the case of two-side projective measurements, and also define a geometric measure on it. Further, a simplified expression and a lower bound of this geometric measure are derived and explicit expressions are obtained for some special cases.
Abstract Measurement-induced nonlocality (MIN), a quantum correlation measure for bipartite systems, is an indicator of maximal global effects due to locally invariant von Neumann projective measurements. It is originally defined as the maximal square of the Hilbert–Schmidt norm of the difference between pre- and post-measurement states. In this article, we propose a new form of MIN based on affinity. This quantity satisfies all the criteria of a bona fide measure of quantum correlation measures. This quantity is evaluated for both arbitrary pure and 2 × n dimensional (qubit–qudit) mixed states. The operational meaning of the proposed quantity is interpreted in terms of the interferometric power of the quantum state. We apply these results on two-qubit mixed states, such as the Werner, isotropic and Bell diagonal states.
Nonlocality is one unique property of quantum mechanics that differs from the classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, known as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose quantifying the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of a completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert–Schmidt norm which may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any -dimensional pure state, two-qubit state, and certain high-dimensional states. As with other quantum correlation measures, the newly defined MIN can be directly applied to various models for physical interpretations.