Quantum jump Monte Carlo approach simplified: Abelian symmetries

Macieszczak, Katarzyna; Rose, Dominic C.

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.

Citation

Macieszczak, K., & Rose, D. C. (2021). Quantum jump Monte Carlo approach simplified: Abelian symmetries. Physical Review A, 103(4), Article 042204. https://doi.org/10.1103/physreva.103.042204

• Journal Article Type: Article
• Acceptance Date: Apr 23, 2021
• Online Publication Date: Apr 5, 2021
• Publication Date: Apr 1, 2021
• Deposit Date: Jun 17, 2021
• Publicly Available Date: Jun 17, 2021
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 103
• Issue: 4
• Article Number: 042204
• DOI: https://doi.org/10.1103/physreva.103.042204
• Public URL: https://nottingham-repository.worktribe.com/output/5690094
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.042204