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This research establishes a general theoretical mechanism explaining the Rényi hierarchy observed in decoherence-induced phase transitions within quantum systems. By leveraging correlation inequalities in replicated statistical models, the study clarifies how critical decoherence strengths scale with the Rényi index across various topological codes and rotor models. These findings advance fundamental understanding of entanglement structure dynamics under noise, which is essential for developing robust quantum error correction strategies.
A Mechanism for the R\'enyi Hierarchy of Decoherence-Induced Phase Transitions
arXiv:2609.30377v1 Announce Type: new 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 R\'enyi index of the entanglement diagnostic, forming a R\'enyi 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 $\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer R\'enyi index $R\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.
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 $\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index $R\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2609.30377 [quant-ph]
(or arXiv:2609.30377v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.30377 arXiv-issued DOI via DataCite (pending registration)
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