# Probing the Full Distribution of Many-Body Observables by Single-Qubit Interferometry

## TL;DR

This paper introduces an experimental method using a single qubit to measure the full distribution of many-body observables in spin systems, enabling insights into equilibrium and non-equilibrium states.

## Contribution

It proposes a novel scheme to extract full distributions of observables via single-qubit interferometry, connecting coherence measurements to the analytically-continued partition function.

## Key findings

- Successful measurement of magnetization distribution
- Determination of kink-number statistics at thermal equilibrium
- Extraction of characteristic functions related to partition functions

## Abstract

We present an experimental scheme to measure the full distribution of many-body observables in spin systems, both in and out of equilibrium, using an auxiliary qubit as a probe. We focus on the determination of the magnetization and the kink-number statistics at thermal equilibrium. The corresponding characteristic functions are related to the analytically-continued partition function. Thus, both distributions can be directly extracted from experimental measurements of the coherence of a probe qubit that is coupled to an Ising-type bath, as reported in [X. Peng et al., Phys. Rev. Lett. 114, 010601 (2015)] for the detection of Lee-Yang zeroes.