Lifting the mixed to the pure: quantum phases of matter from canonical purification

Abstract:Pure-state quantum phases are defined through finite-depth local unitary connections. This concept of phases has recently been generalized to mixed states in terms of locally reversible channels. In this work, we establish a fundamental relation between mixed-state phases and pure-state phases. We show that a locally reversible channel between mixed states can be lifted to a local isometry between their canonical purifications; thus, if two mixed states are in the same phase, then their canonical purifications are in the same pure-state phase. Furthermore, an explicit construction of the lifting isometry is given by ``half'' of the Petz recovery map, suggesting that the Petz recovery map \emph{without rotation} is enough to connect mixed state phases. We illustrate our results with two examples: toric code under bit flip noise and Chern insulator under fermion number noise.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2610.41926 [quant-ph]

(or arXiv:2610.41926v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.41926 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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