Role of quantum state texture in probing resource theories and quantum phase transition

TL;DR

This paper explores how quantum state texture serves as a resource and can signal quantum phase transitions, introducing new monotones and measures applicable across various resource theories.

Contribution

It introduces a texture-based resource monotone applicable to multiple resource theories and demonstrates its effectiveness in detecting quantum phase transitions.

Findings

Difference between maximum and minimum textures is a valid purity monotone.

Proposed a texture-based resource monotone for general convex resource theories.

Texture of ground states signals quantum phase transitions in the Ising model.

Abstract

Building on the recently developed quantum state texture resource theory, we exhibit that the difference between maximum and minimum textures is a valid purity monotone in any dimension and provide a lower bound for existing purity measures. We introduce a texture-based resource monotone applicable across general convex resource theories, encompassing quantum coherence, non-stabilizerness, and entanglement. In particular, we propose the notion of non-local texture, which corresponds to the geometric measure of bipartite and multipartite entanglement in pure states. Furthermore, we demonstrate that the texture of the entire ground state or its subsystems can effectively signal quantum phase transitions in the Ising chain under both transverse and longitudinal magnetic fields, offering a powerful tool for characterizing quantum criticality.