Maximally coherent mixed states: Complementarity between maximal coherence and mixedness

TL;DR

This paper derives an analytical trade-off between quantum coherence and mixedness, identifying maximally coherent mixed states that optimize coherence for a given level of noise, revealing a fundamental complementarity in open quantum systems.

Contribution

It introduces the concept of maximally coherent mixed states and establishes a quantitative trade-off relation between coherence and mixedness.

Findings

Derived an analytical upper bound on quantum coherence for fixed mixedness.

Identified a class of states called maximally coherent mixed states.

Revealed a complementarity relation between coherence and mixedness.

Abstract

Quantum coherence is a key element in topical research on quantum resource theories and a primary facilitator for design and implementation of quantum technologies. However, the resourcefulness of quantum coherence is severely restricted by environmental noise, which is indicated by the loss of information in a quantum system, measured in terms of its purity. In this work, we derive the limits imposed by the mixedness of a quantum system on the amount of quantum coherence that it can possess. We obtain an analytical trade-off between the two quantities that upperbound the maximum quantum coherence for fixed mixedness in a system. This gives rise to a class of quantum states, "maximally coherent mixed states," whose coherence cannot be increased further under any purity-preserving operation. For the above class of states, quantum coherence and mixedness satisfy a complementarity relation, which is crucial to understand the interplay between a resource and noise in open quantum systems.