# Characterization of arbitrary-order correlations in quantum baths by weak measurement

## TL;DR

This paper introduces a method to systematically characterize arbitrary-order correlations in quantum baths using weak measurements, aiding quantum control, sensing, and understanding of decoherence.

## Contribution

It presents a novel scheme employing weak measurements to reconstruct many-body correlations in quantum baths beyond Gaussian approximations.

## Key findings

- Able to reconstruct correlations of arbitrary order in quantum baths
- Includes both classical and quantum parts of correlations
- Facilitates optimization of quantum control and sensing

## Abstract

Correlations of fluctuations are the driving forces behind the dynamics and thermodynamics in quantum many-body systems. For qubits embedded in a quantum bath, the correlations in the bath are the key to understanding and combating decoherence -a critical issue in quantum information technology. However, there is no systematic method for characterizing the many-body correlations in quantum baths beyond the second order or the Gaussian approximation. Here we present a scheme to characterize the correlations in a quantum bath to arbitrary order. The scheme employs weak measurement of the bath via projective measurement of a central system. The bath correlations, including both the "classical" and the "quantum" parts, can be reconstructed from the correlations of the measurement outputs. The possibility of full characterization of many-body correlations in a quantum bath forms the basis for optimizing quantum control against decoherence in realistic environments, for studying the quantum characteristics of baths, and for quantum sensing of correlated clusters in quantum baths.