Compatibility of Quantum Measurements and the Emergence of Classical Objectivity

TL;DR

This paper explores how the classical behavior of quantum systems, as described by Kirkwood-Dirac quasiprobability distributions, emerges when the system's dynamics support Quantum Darwinism, revealing a fundamental link between these concepts.

Contribution

It establishes a fundamental relationship between the classicality of measurement distributions and Quantum Darwinism in quantum systems.

Findings

KDQ distributions become classical if and only if the Hamiltonian supports Quantum Darwinism

Demonstrates a fundamental link between classicality and Quantum Darwinism

Provides conditions under which quantum measurements exhibit classical behavior

Abstract

The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things that it is not always possible to find joint probability distributions which fully capture the joint statistics of multiple measurements. Instead, one must employ more general tools such as the Kirkwood-Dirac quasiprobability (KDQ) distribution, which may exhibit negative or non-real values heralding non-classicality. In this Letter, we consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports Quantum Darwinism. Thus, we demonstrate a fundamental relationship between these two notions of classicality and their emergence in the quantum world.