Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective

Understand

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.