Reconstructing quantum entropy production to probe irreversibility and correlations

Year: 2018

Authors: Gherardini S., Muller MM., Trombettoni A., Ruffo S., Caruso F.

Autors Affiliation: 1 Department of Physics, LENS and QSTAR, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy 2 Department of Information Engineering, University of Florence, via S. Marta 3, I-50139 Florence, Italy 3 INFN, Sezione di Firenze, Sesto Fiorentino, Italy 4 CNR-IOM DEMOCRITOS, via Bonomea 265, I-34136 Trieste, Italy 5 SISSA, via Bonomea 265, I-34136 Trieste, Italy 6 INFN, Sezione di Trieste, I-34151 Trieste, Italy 7 ISC-CNR, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy

Abstract: One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.


Volume: 3 (3)      Pages from: 035013-1  to: 035013-28

More Information: The authors gratefully acknowledge Mauro Paternostro, Giorgio Battistelli, Giacomo Gori, Jin Wang, Francesco Saverio Cataliotti, Duccio Fanelli, Pietro Silvi and Augusto Smerzi for useful discussions. SG and MMM thank the Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy) for hospitality during the completion of this work. AT thanks the Galileo Galilei Institute for Theoretical Physics for the hospitality in the Workshop ´From Static to Dynamical Gauge Fields with Ultracold Atoms´ and the INFN for partial support during the completion of this work. This work was financially supported from Fondazione CR Firenze through the project Q-BIOSCAN.
KeyWords: quantum entropy production, quantum thermodynamics, quantum fluctuation theorem, two-point measurement scheme
DOI: 10.1088/2058-9565/aac7e1