Exploring initial correlations in a Gibbs state by local application of external field

TL;DR

This paper shows that applying a weak local external field can reveal initial correlations in a quantum system by increasing the distinguishability between correlated and uncorrelated states, breaking the usual contractivity property.

Contribution

It introduces a method to detect initial system-environment correlations through local external fields, demonstrating increased state distinguishability in a specific quantum model.

Findings

Trace distance increases with external field application

Initial correlations can be detected via local perturbations

Contractivity of quantum states can break down under local fields

Abstract

We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We evaluate the trace distance (or, equivalently, the Hilbert-Schmidt distance) between the quantum states which evolve from two kinds of initial states; the correlated Gibbs state and its uncorrelated marginal state. We find that the trace distance increases above its initial value for any and all parameter settings. This indicates that we can explore the existence of initial system-environment correlations with applying a local external field, which causes the breakdown of the contractivity.