A Unified Framework for Locally Stable Phases

Fuente: arXiv
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Main Authors: Li, Zhi, Firanko, Raz, Hsieh, Timothy H.
Format: Preprint
Published: 2026
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author Li, Zhi
Firanko, Raz
Hsieh, Timothy H.
author_facet Li, Zhi
Firanko, Raz
Hsieh, Timothy H.
contents We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short range correlated, defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of a family of nonlinear correlators, including the fidelity correlator, and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable (short range correlated) states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.
format Preprint
id arxiv_https___arxiv_org_abs_2605_00088
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Unified Framework for Locally Stable Phases
Li, Zhi
Firanko, Raz
Hsieh, Timothy H.
Quantum Physics
Statistical Mechanics
Mathematical Physics
We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short range correlated, defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of a family of nonlinear correlators, including the fidelity correlator, and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable (short range correlated) states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.
title A Unified Framework for Locally Stable Phases
topic Quantum Physics
Statistical Mechanics
Mathematical Physics
url https://arxiv.org/abs/2605.00088