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

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.