Quasiprobabilities in Quantum Thermodynamics and Many-Body Systems

Year: 2024

Authors: Gherardini S., De Chiara G.

Autors Affiliation: Ist Nazl Ott Consiglio Nazl Ric CNR INO, Largo Enrico Fermi 6, I-50125 Florence, Italy; Univ Firenze, European Lab Nonlinear Spect, I-50019 Sesto Fiorentino, Italy; Queens Univ Belfast, Ctr Quantum Mat & Technol, Sch Math & Phys, Belfast BT7 1NN, North Ireland.

Abstract: In this tutorial, we present the definition, interpretation, and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the incompatibility of the measurement observables and the state of the measured quantum system. We particularly focus on Kirkwood-Dirac quasiprobabilities and related distributions. We also discuss techniques to experimentally access a quasiprobability distribution, ranging from the weak two-point measurement scheme, to a Ramsey-like interferometric scheme and procedures assisted by an external detector. Once defined the fundamental concepts following the standpoint of joint measurability in quantum mechanics, we illustrate the use of quasiprobabilities in quantum thermodynamics to describe the quantum statistics of work and heat, and to explain anomalies in the energy exchanges entailed by a given thermodynamic transformation. On the one hand, in work protocols, we show how absorbed energy can be converted to extractable work and vice versa due to Hamiltonian incompatibility at distinct times. On the other hand, in exchange processes between two quantum systems initially at different temperatures, we explain how quantum correlations in their initial state may induce cold-to-hot energy exchanges, which are unnatural between any pair of equilibrium nondriven systems. We conclude the tutorial by giving simple examples where quasiprobabilities are applied to many-body systems: scrambling of quantum information, sensitivity to local perturbations, and quantum work statistics in the quenched dynamics of models that can be mapped onto systems of free fermions, for instance, the Ising model with a transverse field. Throughout the tutorial, we meticulously present derivations of essential concepts alongside straightforward examples, aiming to enhance comprehension and facilitate learning.

Journal/Review: PRX QUANTUM

Volume: 5 (3)      Pages from: 30201-1  to: 30201-38

More Information: We acknowledge enlightening discussions with Kenza Hammam, Paolo Solinas, and Nicole Yunger-Halpern. S.G. acknowledges financial support from the project PRIN 2022 Quantum Reservoir Computing (QuReCo) , the PNRR MUR project PE0000023-NQSTI financed by the European Union-Next Generation EU, the MISTI Global Seed Funds MIT-FVG Collaboration Grant Revealing and exploiting quantumness via quasiprobabilities: from quantum thermodynamics to quantum sensing, and the Royal Society Project IES R 3223086 Dissipation-based quantum inference for out-of-equilibrium quantum many-body systems. G.D.C. acknowledges support from the UK EPSRC through Grant No. EP/S0299 4X/1.
KeyWords: Counting Statistics; Model
DOI: 10.1103/PRXQuantum.5.030201