Mixed state topological order: operator algebraic approach

2025/01/04 by Yoshiko Ogata, Ogata, Yoshiko · 3 citations
Business, Management and Accounting · Engineering · #Advanced Research in Systems and Signal Processing #FOS: Physical sciences #Mathematical Physics (math-ph) #Optics and Image Analysis #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2501.02398

openalex publication_date 2025/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided C^*-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided C^*-tensor category of the final state is a braided C^*-tensor subcategory of the initial state.

Cited by

• Stacking and the triviality of invertible phases
• Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases
• Topological Mixed States: Phases of Matter from Axiomatic Approaches

Related

• Boundary states of a bulk gapped ground state in 2-d quantum spin systems
• New Invariants and Separability criterion of the Mixed States: Bipartite Case
• Topological Mixed States: Phases of Matter from Axiomatic Approaches
• New Invariants and Separability Criterion of the Mixed States: Multipartite Case
• Tensor network formulation of symmetry protected topological phases in mixed states