Measurement-induced nonlocality based on the trace norm

Abstract

Nonlocality is one unique property of quantum mechanics differing from classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, termed as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose to quantify the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of 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 that 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 2 × n dimensional pure state, two-qubit state, and certain high-dimensional states. As other quantum correlation measures, the new defined MIN can be directly applied to various models for physical interpretations.

Entropic Uncertainty in Neutrino and Meson Systems

“…[27] To discuss the relationship between the entropic uncertainty and the quantum correlation, we employ trace norm measurement-induced nonlocality [28] as the measure of quantum correlation. Quantum correlation is beyond entanglement which plays key role in quantum information field.…”

“…The analytic formula for calculating trace norm measurement-induced nonlocality of the state (4) is [28] The local unitary invariance of the quantum correlation measure guarantees Q( ) = Q(ρ).…”

Evolution equation for geometric quantum correlation measures

“…(iii) If opt represents maximum and M is confined to the locally invariant measurements that maintain ρ a , Eq. (3) turns to be the conventional measurement-induced nonlocality for p = 2 [20], and its modified version for p = 1 [21]. Besides D p (ρ) that is determined by x, y, and the matrix T = (t ij ), there are other measures related to explicit quantum protocols that are determined solely by T .…”

Analytically Computable Symmetric Quantum Correlations

“…Therefore, the most fruitful approach is to focus on effective quantification only for states in certain specific classes. [42][43][44][45][46][47][48][49] However, neither the QD nor the MIN of a bipartite system is symmetric in the sense that different results will be obtained (especially for some zero-discord states) if the two subsystems are swapped, which implies that the QD and MIN cannot completely quantify all of the quantum correlations present in a state. [26][27][28][29][30][31][32][33][34][35][36][37][38][39] The same is true for its counterpart quantity, [40][41][42] that is, the measurementinduced nonlocality (MIN) which characterizes the global disturbance in a composite state caused by a local nondisturbing measurement on one subsystem.…”