Measurement-induced nonlocality based on the relative entropy

TL;DR

This paper introduces a new way to measure measurement-induced nonlocality using relative entropy, providing operational meaning, bounds, and relations to other nonlocality measures, with explicit formulas for specific states.

Contribution

It defines the relative entropy of nonlocality, relates it to geometric nonlocality and entanglement, and derives explicit formulas and trade-off relations.

Findings

Relative entropy of nonlocality is bounded by the entropy of the measured subsystem.

It equals the maximal distillable entanglement.

Explicit formulas are provided for Bell-diagonal states.

Abstract

We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy of the measured subsystem. We establish a relationship between the relative entropy of nonlocality and the geometric nonlocality based on the Hilbert- Schmidt norm, and show that it is equal to the maximal distillable entanglement. Several trade-off relations are obtained for tripartite pure states. We also give explicit expressions for the relative entropy of nonlocality for Bell-diagonal states.