Quantum jump Monte Carlo simplified: Abelian symmetries

Abstract

We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the dynamics. We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio. In turn, this representation simplifies both the construction of the master operator as well as quantum jump Monte Carlo simulations, where, for a symmetric initial state, stochastic trajectories of the system state are supported within a single symmetry eigenspace at a time, which is changed only by the action of an asymmetric jump operator. Our results generalize directly to the case of multiple Abelian weak symmetries.

arXiv commentPublished version (12 pages, 8 figures)

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Cited by in corpus (4)

• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Edge modes and symmetry-protected topological states in open quantum systems
• Symmetry-resolved entanglement in fermionic systems with dissipation
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?