Non-Local Advantage of Quantum Coherence

TL;DR

This paper establishes complementarity relations between quantum coherences in mutually unbiased bases and identifies conditions for non-local advantage of quantum coherence, contributing to understanding quantum steerability.

Contribution

It introduces new complementarity relations for quantum coherence and delineates conditions for non-local advantage, advancing the study of quantum steerability.

Findings

Not all steerable states exhibit non-local advantage of coherence.

Derived conditions specify when non-local coherence advantage is achievable.

Complementarity relations link coherence measures to steerability criteria.

Abstract

A bipartite state is said to be steerable if and only if it does not have a single system description, i.e., the bipartite state cannot be explained by a local hidden state model. Several steering inequalities have been derived using different local uncertainty relations to verify the ability to control the state of one subsystem by the other party. Here, we derive complementarity relations between coherences measured on mutually unbiased bases using various coherence measures such as the $l_1$-norm, relative entropy and skew information. Using these relations, we derive conditions under which non-local advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such advantage.