Interferometry of quantum correlation functions to access quasiprobability distribution of work

TL;DR

This paper demonstrates an interferometric method to reconstruct the Kirkwood-Dirac quasiprobability distribution of work in a quantum system, providing insights into quantum thermodynamics and measurement uncertainties.

Contribution

It introduces an experimental scheme using an auxiliary system to reconstruct the quasiprobability distribution of work in a quantum system, advancing quantum thermodynamics research.

Findings

Successfully reconstructed the work quasiprobability distribution in a nitrogen-vacancy center.

Analyzed the moments and physical meaning of the distribution in quantum thermodynamics.

Studied measurement uncertainties using the Robertson-Schrödinger relation for different states.

Abstract

The Kirkwood-Dirac quasiprobability distribution, intimately connected with the quantum correlation function of two observables measured at distinct times, is becoming increasingly relevant for fundamental physics and quantum technologies. This quasiprobability distribution can take non-positive values, and its experimental reconstruction becomes challenging when expectation values of incompatible observables are involved. Here, we use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. We experimentally demonstrate this scheme in an electron-nuclear spin system associated with a nitrogen-vacancy center in diamond. By measuring the characteristic function, we reconstruct the quasiprobability distribution of work and analyze the behavior of its first and second moments. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics. Finally, we study the uncertainty of measuring the Hamiltonian of the system at two times, via the Robertson-Schr{\"o}dinger uncertainty relation, for different initial states.