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

Abstract

The thermodynamic behavior ofMarkovian 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.We wish to acknowledge support from the María de Maeztu project (CEX2021-001164-M) for Units of Excellence, QUARESC project (PID2019-109094GB-C21), CoQuSy project (PID2022-140506NB-C21) and QuTTNAQMa project (PID2020-117347GB-I00), funded by the Spanish State Research Agency MCIN/AEI/10.13039/501100011033 and FEDER, UE. G.M. is supported through the Ramón y Cajal program (RYC2021-031121-I) funded by MCIN/AEI/10.13039/501100011033 and European Union NextGenerationEU/PRTR. R.L. acknowledges the financial support by the Grant No. PDR2020/12 sponsored by Comunitat Autonoma de les Illes Balears through the “Direcció General de Política Universitaria i Recerca” with funds from the Tourist Stay Tax Law ITS 2017-006 and the Grant No. LINKB20072 from the CSIC i-link program 2021. M.F.C. also acknowledges funding from Generalitat Valenciana (CIACIF/2021/434)