A Unified Framework for Locally Stable Phases
Abstract
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.
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BibTeX
@misc{li2026unified,
title = {{A Unified Framework for Locally Stable Phases}},
author = {Zhi Li and Raz Firanko and Timothy H. Hsieh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.00088},
eprint = {2605.00088},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00088},
}
RIS
TY - UNPB
TI - A Unified Framework for Locally Stable Phases
AU - Zhi Li
AU - Raz Firanko
AU - Timothy H. Hsieh
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.00088
UR - https://arxiv.org/abs/2605.00088
AB - 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.
ER -