Quantifying and detecting quantum-state texture

TL;DR

This paper introduces a new measure for quantum-state texture, explores its properties and relationships with existing measures, and develops detection methods using texture witnesses.

Contribution

It constructs a novel texture measure based on Rényi relative entropy, analyzes relationships among measures, and introduces texture witnesses for detection.

Findings

Proposed a new texture measure $\,\mathcal{T}^{\text{GR}}_{\alpha,z}$ based on Rényi entropy.

Established mathematical relationships among various texture measures.

Developed texture witnesses for detecting quantum-state texture.

Abstract

Quantum-state texture is a recently proposed quantum resource that characterizes the inhomogeneity of a quantum state's matrix element distribution in the computational basis, enriching our understanding of quantum state structure. To expand its quantification toolkit and establish detection methods, in this article, we investigate the resource theory of texture from both quantitative and detection perspectives. First, we construct a texture measure $\mathcal{T}^{\text{GR}}_{\alpha,z}(\rho)$ based on the $\alpha$-$z$ R\'enyi relative entropy and present some of its inherent properties. Second, we analyze the mathematical relationships between several existing texture measures, revealing connections among different quantifiers. Finally, drawing on the witness concept from other resource theories, we systematically introduce texture witnesses into the texture theory and provide examples of texture witnesses with special properties.