Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection

Abstract

The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the definition of main thermodynamic quantities becomes subtle and universal fluctuation relations are unknown. Here, we fill this gap by deriving a universal fluctuation relation that links thermodynamic entropy production and information-theoretical irreversibility along single trajectories in inefficient monitoring setups. This relation provides as a corollary an irreversibility estimator of dissipation using imperfect detection records that lower bounds the underlying entropy production at the level of visible trajectories. We illustrate our findings with a driven-dissipative two-level system following quantum jump trajectories and discuss the experimental applicability of our results for thermodynamic inference.

5 + 12 pages, 3 figures. The two first authors contributed equally to this work. v2: minor changes, figure added, references added. v3: 8 + 5 pages, 3 figures. New distribution of material, expanded discussions, improved presentation, references added and title modified (accepted in PRR)

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Cited by in corpus (5)

• Roadmap on Quantum Thermodynamics
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Compensating random transition-detection blackouts in Markov networks
• Coarse-grained quantum thermodynamics: Observation-dependent quantities, observation-independent laws
• Quantum Measurement Induced Radiative Processes in Continuously Monitored Optical Environments