Measurement-induced nonlocality over two-sided projective measurements

TL;DR

This paper introduces a two-sided measurement-induced nonlocality (MiN) for bipartite quantum systems, characterizes its nullity, provides formulas for pure states, bounds for mixed states, and compares it with geometric quantum discord in finite and infinite dimensions.

Contribution

It extends MiN to two-sided projective measurements, offers a nullity characterization, and compares it with geometric quantum discord across dimensions.

Findings

Two-sided MiN is not continuous.

Formulas for pure states are proposed.

Lower bounds for maximally entangled mixed states are given.

Abstract

Measurement-induced nonlocality (MiN), introduced by Luo and Fu [Phys. Rev. Lett. 106(2011)120401], is a kind of quantum correlation that beyond entanglement and even beyond quantum discord. Recently, we extended MiN to infinite-dimensional bipartite system [arXiv:1107.0355]. MiN is defined over one-sided projective measurements. In this letter we introduce a measurement-induced nonlocality 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. The two-sided geometric measure of quantum discord (GMQD) is introduced in [Phys. Lett. A 376(2012)320--324]. We extend it to infinite-dimensional system and then compare it with the two-sided MiN. Both finite- and infinite-dimensional cases are considered.