Quantum processes which do not use coherence

TL;DR

This paper characterizes quantum operations that do not utilize coherence, providing a physical interpretation, a dilation theorem, and exploring implications for quantum correlations and discord.

Contribution

It introduces a physically motivated class of coherence-free quantum operations and links coherence to quantum discord and correlations.

Findings

Defined operations that do not exploit coherence

Proved a dilation theorem for these operations

Linked coherence with quantum discord and correlations

Abstract

A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalisation of incoherent operations -- those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem, showing how these operations can always be constructed by interacting the system in an incoherent way with an ancilla. Such a physical justification is not known for the incoherent operations, thus our results lead to a physically well-motivated resource theory of coherence. Next, we investigate the implications for coherence in multipartite systems. We show that quantum correlations can be defined naturally with respect to a fixed basis, providing a link between coherence and quantum discord. We demonstrate the interplay between these two quantities under our studied operations, and suggest implications for the theory of quantum discord by relating the studied operations to those which cannot create discord.