Maximally coherent states and coherence-preserving operations

TL;DR

This paper refines the quantification of quantum coherence by defining maximally coherent states and coherence-preserving operations, establishing criteria that improve the validity and efficiency of coherence measures.

Contribution

It introduces a measure-independent definition of maximally coherent states and coherence-preserving operations, enhancing the framework for quantifying quantum coherence.

Findings

Maximally coherent states can generate all states of the same dimension via incoherent operations.

Only maximally coherent states should attain the maximum value for any valid coherence measure.

The new criteria exclude invalid or inefficient coherence measures.

Abstract

We investigate the maximally coherent states to provide a refinement in quantifying coherence and give a measure-independent definition of the coherence-preserving operations. A maximally coherent state can be considered as the resource to create arbitrary quantum states of the same dimension by merely incoherent operations. We propose that only the maximally coherent states should achieve the maximal value for a coherence measure and use this condition as an additional criterion for coherence measures to obtain a refinement in quantifying coherence which excludes the invalid and inefficient coherence measures. Under this new criterion, we then give a measure-independent definition of the coherence-preserving operations, which play a similar role in quantifying coherence as that played by the local unitary operations in the scenario of studying entanglement.