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

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.

v2: 12 pages and 3 figures, with minor changes and close to the published version

References in corpus (14)

• Sudden Death of Entanglement
• Measuring Quantum Coherence with Entanglement
• Quantum discord and quantum phase transition in spin chains
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Linking a distance measure of entanglement to its convex roof
• The quantum Ising chain for beginners
• Stabilizer entropies are monotones for magic-state resource theory
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Quantum-state texture and gate identification
• All entangled states are quantum coherent with locally distinguishable bases
• Quantum metrology and coherence
• Resource Theory of Non-absolute Separability
• Coherence measure of ensembles with nonlocality without entanglement
• Measuring polynomial functions of states