Unraveling the large deviation statistics of Markovian open quantum systems

Carollo, Federico; Jack, Robert L.; Garrahan, Juan P.

Abstract

We analyze dynamical large deviations of quantum trajectories in Markovian open quantum systems in their full generality. We derive a quantum level-2.5 large deviation principle for these systems, which describes the joint fluctuations of time-averaged quantum jump rates and of the time-averaged quantum state for long times. Like its level-2.5 counterpart for classical continuous-time Markov chains (which it contains as a special case), this description is both explicit and complete, as the statistics of arbitrary time-extensive dynamical observables can be obtained by contraction from the explicit level-2.5 rate functional we derive. Our approach uses an unraveled representation of the quantum dynamics which allows these statistics to be obtained by analyzing a classical stochastic process in the space of pure states. For quantum reset processes we show that the unraveled dynamics is semi-Markovian and derive bounds on the asymptotic variance of the number of quantum jumps which generalize classical thermodynamic uncertainty relations. We finish by discussing how our level-2.5 approach can be used to study large deviations of nonlinear functions of the state, such as measures of entanglement.

Citation

Carollo, F., Jack, R. L., & Garrahan, J. P. (2019). Unraveling the large deviation statistics of Markovian open quantum systems. Physical Review Letters, 122(13), Article 130605. https://doi.org/10.1103/physrevlett.122.130605

• Journal Article Type: Article
• Acceptance Date: Mar 13, 2019
• Online Publication Date: Apr 5, 2019
• Publication Date: Apr 5, 2019
• Deposit Date: Apr 29, 2019
• Publicly Available Date: Apr 5, 2019
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 122
• Issue: 13
• Article Number: 130605
• DOI: https://doi.org/10.1103/physrevlett.122.130605
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/1849798
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.130605
• Additional Information: Unraveling the Large Deviation Statistics of Markovian Open Quantum Systems, Federico Carollo, Robert L. Jack, and Juan P. Garrahan,; Phys. Rev. Lett. 122, 130605.