Quasiprobabilities in quantum thermodynamics and many-body systems: A tutorial

Quasiprobabilities in quantum thermodynamics and many-body systems: A tutorial

March 27, 2024 | Stefano Gherardini and Gabriele De Chiara
This tutorial provides a comprehensive overview of quasiprobabilities and their applications in quantum thermodynamics and many-body systems. Quasiprobabilities are mathematical quantities that describe the statistics of measurement outcomes at two or more times, incorporating the incompatibility of measurement observables and the state of the quantum system. The tutorial covers the definition, interpretation, and properties of quasiprobabilities, including the no-go theorem for sequential outcomes statistics and the introduction of quasiprobability distributions (QD) that can be non-positive or complex. It discusses experimental techniques to access QD distributions, such as the weak two-point measurement scheme, interferometric schemes, and detector-assisted measurements. The tutorial also explores the use of quasiprobabilities in quantum thermodynamics to describe the quantum statistics of work and heat, and to explain anomalies in energy exchanges. Additionally, it delves into the application of quasiprobabilities in many-body systems, including quantum scrambling, out-of-time-ordered correlators, and quantum work statistics in models like the Ising model with a transverse field. The tutorial aims to enhance understanding and facilitate learning through detailed derivations and examples.This tutorial provides a comprehensive overview of quasiprobabilities and their applications in quantum thermodynamics and many-body systems. Quasiprobabilities are mathematical quantities that describe the statistics of measurement outcomes at two or more times, incorporating the incompatibility of measurement observables and the state of the quantum system. The tutorial covers the definition, interpretation, and properties of quasiprobabilities, including the no-go theorem for sequential outcomes statistics and the introduction of quasiprobability distributions (QD) that can be non-positive or complex. It discusses experimental techniques to access QD distributions, such as the weak two-point measurement scheme, interferometric schemes, and detector-assisted measurements. The tutorial also explores the use of quasiprobabilities in quantum thermodynamics to describe the quantum statistics of work and heat, and to explain anomalies in energy exchanges. Additionally, it delves into the application of quasiprobabilities in many-body systems, including quantum scrambling, out-of-time-ordered correlators, and quantum work statistics in models like the Ising model with a transverse field. The tutorial aims to enhance understanding and facilitate learning through detailed derivations and examples.
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