Measurement-induced nonlocality based on the trace norm

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 (2× n)-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.