A Mechanism for the Rényi Hierarchy of Decoherence-Induced Phase Transitions
Abstract
Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in ℤ2 topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong U(1) symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index R≥2. We show that this mechanism also applies to a class of models with correlated decoherence.
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BibTeX
@misc{yang2026mechanism,
title = {{A Mechanism for the Rényi Hierarchy of Decoherence-Induced Phase Transitions}},
author = {Zhou Yang and Yuri D. Lensky and Chao-Ming Jian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30377},
eprint = {2609.30377},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30377},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Mechanism for the Rényi Hierarchy of Decoherence-Induced Phase Transitions
AU - Zhou Yang
AU - Yuri D. Lensky
AU - Chao-Ming Jian
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30377
UR - https://arxiv.org/abs/2609.30377
AB - Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in ℤ_2 topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong U(1) symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index R≥2. We show that this mechanism also applies to a class of models with correlated decoherence.
ER -