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Equivalence of states and bimodule quantum channels

  • Linzhe Huang
  • Chunlan Jiang
  • Zhengwei Liu
  • Jinsong Wu
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Abstract

We study the action of quantum channels on states on a von Neumann algebra ℳ with conserved quantities encoded by a subalgebra 𝒩. We define a phase as an equivalence class of normal states on ℳ under the action of quantum channels preserving 𝒩. First, we establish a relative quasi-entropic characterization of phase equivalence using the Petz recovery map. We further introduce the operator algebra (OA) symmetry of a state and define an equivalence relation between OA symmetries via bishifts of biprojections. When 𝒩⊆ℳ is an irreducible finite-index subfactor of type II1, we prove that phase equivalence implies OA symmetry equivalence. Consequently, OA symmetry breaking provides a sufficient mechanism for detecting phase transitions. Furthermore, combining finite-index subfactor theory with quantum Fourier analysis, we prove that the cardinality of each phase is finite and obtain an explicit upper bound depending only on the Jones index.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026equivalence,
  title = {{Equivalence of states and bimodule quantum channels}},
  author = {Linzhe Huang and Chunlan Jiang and Zhengwei Liu and Jinsong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20879},
  eprint = {2609.20879},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20879},
}
RIS
TY  - UNPB
TI  - Equivalence of states and bimodule quantum channels
AU  - Linzhe Huang
AU  - Chunlan Jiang
AU  - Zhengwei Liu
AU  - Jinsong Wu
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.20879
UR  - https://arxiv.org/abs/2609.20879
AB  - We study the action of quantum channels on states on a von Neumann algebra ℳ with conserved quantities encoded by a subalgebra 𝒩. We define a phase as an equivalence class of normal states on ℳ under the action of quantum channels preserving 𝒩. First, we establish a relative quasi-entropic characterization of phase equivalence using the Petz recovery map. We further introduce the operator algebra (OA) symmetry of a state and define an equivalence relation between OA symmetries via bishifts of biprojections. When 𝒩⊆ℳ is an irreducible finite-index subfactor of type II_1, we prove that phase equivalence implies OA symmetry equivalence. Consequently, OA symmetry breaking provides a sufficient mechanism for detecting phase transitions. Furthermore, combining finite-index subfactor theory with quantum Fourier analysis, we prove that the cardinality of each phase is finite and obtain an explicit upper bound depending only on the Jones index.
ER  -