Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective

TL;DR

This paper investigates how decoherence and symmetry breaking in mixed quantum states can be understood through purification, revealing connections to symmetry-protected topological order and long-range correlations.

Contribution

It introduces a purification framework to analyze decoherence-induced symmetry breaking and maps mixed-state order to SPT order in an extended Hilbert space.

Findings

Mixed-state long-range order maps to SPT order in purification

Fidelity correlators in mixed states correspond to strange correlators in purification

Purification approach extends to mixed-state topological phases

Abstract

We explore the landscape of the decoherence effect in mixed-state ensembles from a purification perspective. We analyze the spontaneous strong-to-weak symmetry breaking (SSSB) in mixed states triggered by local quantum channels by mapping this decoherence process to unitary operations in the purified state within an extended Hilbert space. Our key finding is that mixed-state long-range order and SSSB can be mapped into symmetry-protected topological (SPT) order in the purified state. Notably, the measurement-induced long-range order in the purified SPT state mirrors the long-range order in the mixed state due to SSSB, characterized by the Renyi-2 correlator. We establish a correspondence between fidelity correlators in the mixed state, which serve as a measure of SSSB, and strange correlators in the purification, which signify the SPT order. This purification perspective is further extended to explore intrinsic mixed-state topological order and decoherent symmetry-protected topological phases.