Distance between quantum states in presence of initial qubit-environment correlations: a comparative study

TL;DR

This paper compares how different distance measures between quantum states evolve over time in open quantum systems with initial correlations, highlighting the impact of initial system-environment correlations on quantum state distinguishability.

Contribution

It provides a comparative analysis of multiple distance measures' behavior in quantum systems with initial correlations, revealing their dependence on the environment's size and structure.

Findings

Trace distance can increase due to initial correlations.

Different distance measures exhibit distinct behaviors over time.

Environment size influences the evolution of quantum state distances.

Abstract

The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert- Schmidt distance, the Bures distance, the Hellinger distance and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bi-linearly coupled to an infinite and a finite size environment with the latter composed of harmonic oscillators.