The classical correlation limits the ability of the measurement-induced average coherence

TL;DR

This paper investigates how classical correlations limit the maximum average coherence gained through measurements on bipartite quantum states, revealing that classical correlation bounds this coherence rather than quantum correlation.

Contribution

It establishes that the maximal extra average coherence is bounded by classical correlation, providing conditions for zero maximal extra coherence and clarifying the roles of quantum and classical correlations.

Findings

Maximal extra average coherence is upper bounded by classical correlation.

Quantum correlation is neither sufficient nor necessary for nonzero extra coherence.

Conditions for null maximal extra average coherence are identified.

Abstract

Coherence is the most fundamental quantum feature in quantum mechanics. For a bipartite quantum state, if a measurement is performed on one party, the other party, based on the measurement outcomes, will collapse to a corresponding state with some probability and hence gain the average coherence. It is shown that the average coherence is not less than the coherence of its reduced density matrix. In particular, it is very surprising that the extra average coherence (and the maximal extra average coherence with all the possible measurements taken into account) is upper bounded by the classical correlation of the bipartite state instead of the quantum correlation. We also find the sufficient and necessary condition for the null maximal extra average coherence. Some examples demonstrate the relation and, moreover, show that quantum correlation is neither sufficient nor necessary for the nonzero extra average coherence within a given measurement. In addition, the similar conclusions are drawn for both the basis-dependent and the basis-free coherence measure.