Symmetry Breaking and Error Correction in Open Quantum Systems

2020/08/06 by Simon Lieu, Ron Belyansky, Jeremy T. Young +3 · 114 citations
Computer Science · Mathematics · Physics and Astronomy · #Explicit symmetry breaking #Geometry #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum many-body systems #Quantum mechanics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Theoretical physics #cond-mat.mes-hall #cond-mat.quant-gas #physics.optics #quant-ph

paper · pdf · doi:10.1103/physrevlett.125.240405

published in Physical Review Letters 125(24), 240405 (American Physical Society) · 5 + 6 pages

arxiv created 2020/08/06 · openalex publication_date 2020/12/08 · arxiv updated 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_n symmetry-breaking transitions for both cases. In the case of Z₂, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.

Citations

• Continuous quantum error correction for non-Markovian decoherence
• Information-preserving structures: A general framework for quantum zero-error information
• Completely positive dynamical semigroups of N-level systems
• Nonequilibrium Quantum Condensation in an Incoherently Pumped Dissipative System
• Dynamical phase transition in the open Dicke model
• Emergence of spontaneous symmetry breaking in dissipative lattice systems
• Exact results for Schrödinger cats in driven-dissipative systems and their feedback control
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Symmetry-protected coherent relaxation of open quantum systems

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• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation