Inferring work by quantum superposing forward and time-reversal evolutions

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Rubino, Giulia
Manzano, Gonzalo
Rozema, Lee A.
Walther, Philip
Brukner, Caslav
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The study of thermodynamic fluctuations allows one to relate the free energy difference between two equilibrium states with the work done on a system through processes far from equilibrium. This finding plays a crucial role in the quantum regime, where the definition of work becomes nontrivial. Based on these relations, here we develop a simple interferometric method allowing a direct estimation of the work distribution and the average dissipative work during a driven thermodynamic process by superposing the forward and time-reversal evolutions of the process. We show that our scheme provides useful upper bounds on the average dissipative work even without full control over the thermodynamic process, and we propose methodological variations depending on the possible experimental limitations encountered. Finally, we exemplify its applicability by an experimental proposal for implementing our method on a quantum photonics system, on which the thermodynamic process is performed through polarization rotations induced by liquid crystals acting in a discrete temporal regime.
The authors wish to thank the organizers of the conference "New Directions in Quantum Information" (Nordita, Stock-holm; April 1-26, 2019) for providing a stimulating platform for the discussion which originated this result. G.R. ac-knowledges financial support from the Royal Society through Newton International Fellowship No. NIF\R1\202512. G.M. acknowledges funding from the Spanish MICINN through the Juan de la Cierva program (IJC2019-039592-I) and the European Union's Horizon 2020 research and innovation pro-gram under Marie Skodowska-Curie Grant Agreement No. 801110 and the Austrian Federal Ministry of Education, Sci-ence and Research (BMBWF) . L.A.R. acknowledges financial support from the Austrian Science Fund (FWF) through Be-yondC (F7113) . P.W. acknowledges financial support from the research platform TURIS, from the European Commis-sion through EPIQUS (No. 899368) , and from the Austrian Science Fund via GRIPS (P30817-N36) , BeyondC (F7113) , and Research Group 5 (FG5) . J.M.R.P. acknowledges finan-cial support from the Spanish Government (Grant Contract No. FIS-2017-83706-R) . C?.B. acknowledges financial support from the Austrian Science Fund (FWF) through the SFB project BeyondC (Subproject No. F7103) , a grant from the Foundational Questions Institute (FQXi) Fund, and from the European Commission via Testing the Large-Scale Limit of Quantum Mechanics (TEQ) (No. 766900) project. This publi-cation was made possible through the support of Grant No. ID61466 from the John Templeton Foundation, as part of the the Quantum Information Structure of Spacetime (QISS) Project [59] . The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.
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