An Observable-Algebra Approach to Quantum Coherence in Anyonic Systems
Abstract
Physical restrictions on operations can make quantum coherence inaccessible. Quantifying off-diagonal density matrix elements in a chosen basis alone does not reveal which information is hidden by each restriction. To distinguish their effects, we describe physical restrictions through subalgebras of accessible observables. The associated trace-preserving conditional expectations unify two reconstruction principles: each gives both the maximum-entropy state compatible with the accessible data and the closest state in the corresponding subalgebra in relative entropy. We apply this framework to anyonic systems to separate the contributions from local-charge superselection and non-Abelian fusion rules. We prove that the charge-line severing map is the conditional expectation onto the local-product subalgebra. It is completely positive and quantum-trace-preserving, and uniquely reconstructs a state in this space from all local-product expectation values. The hierarchy of measurement restrictions then separates total bipartite coherence into three nonnegative contributions: coherence between local charges, inaccessible fusion information, and conventional coherence. The first two decompose the anyonic charge entanglement and distinguish the effects of local-charge superselection from the remaining fusion information. Finally, we relate basis-independent measures of anyonic coherence to entanglement. For pure anyonic states with vacuum total charge, the optimized total and correlated coherence equal the total and conventional relative-entropy entanglement, respectively.
Related
- Closed-Relational Reconstruction Systems: Viability, Observable-History Lifting, and Finite Obstruction Certificates
- Using delays for prescribed-time static output feedback stabilization of LTI controllable and observable systems
- Persistence collapse transitions and observable admissibility in nonlinear dynamical systems: a preregistered empirical benchmark
- On the quantum super Virasoro algebra
- From the quantum group Uq1/2( sl̂2 ) to the Kronecker quantum cluster algebra
BibTeX
@misc{xu2026observablealgebra,
title = {{An Observable-Algebra Approach to Quantum Coherence in Anyonic Systems}},
author = {Cheng-Qian Xu and D. L. Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01749},
eprint = {2611.01749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01749},
note = {CC0},
}
RIS
TY - UNPB
TI - An Observable-Algebra Approach to Quantum Coherence in Anyonic Systems
AU - Cheng-Qian Xu
AU - D. L. Zhou
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01749
UR - https://arxiv.org/abs/2611.01749
AB - Physical restrictions on operations can make quantum coherence inaccessible. Quantifying off-diagonal density matrix elements in a chosen basis alone does not reveal which information is hidden by each restriction. To distinguish their effects, we describe physical restrictions through subalgebras of accessible observables. The associated trace-preserving conditional expectations unify two reconstruction principles: each gives both the maximum-entropy state compatible with the accessible data and the closest state in the corresponding subalgebra in relative entropy. We apply this framework to anyonic systems to separate the contributions from local-charge superselection and non-Abelian fusion rules. We prove that the charge-line severing map is the conditional expectation onto the local-product subalgebra. It is completely positive and quantum-trace-preserving, and uniquely reconstructs a state in this space from all local-product expectation values. The hierarchy of measurement restrictions then separates total bipartite coherence into three nonnegative contributions: coherence between local charges, inaccessible fusion information, and conventional coherence. The first two decompose the anyonic charge entanglement and distinguish the effects of local-charge superselection from the remaining fusion information. Finally, we relate basis-independent measures of anyonic coherence to entanglement. For pure anyonic states with vacuum total charge, the optimized total and correlated coherence equal the total and conventional relative-entropy entanglement, respectively.
ER -