Coherence-mixedness trade-offs

TL;DR

This paper establishes basis-independent constraints on quantum coherence based on mixedness, revealing fundamental limits on coherence resources in noisy quantum systems and generalizing previous basis-dependent relations.

Contribution

It introduces basis-independent coherence-mixedness trade-offs using multiple measures, advancing understanding of coherence under environmental noise in quantum systems.

Findings

Derived basis-independent coherence constraints

Generalized prior basis-dependent relations

Quantified limits on coherence extraction in noisy environments

Abstract

Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the $l_2$ norm coherence, conditional von Neumann entropy and Wigner-Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise.