Nonlocal advantage of quantum coherence

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 a nonlocal advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such an advantage.