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

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.

References in corpus (6)

• Properties of Classical and Quantum Jensen-Shannon Divergence
• On the metric character of the quantum Jensen-Shannon divergence
• Witness for initial system-environment correlations in open system dynamics
• Initial correlations in open system's dynamics: The Jaynes-Cummings model
• Experimental investigation of initial system-environment correlations via trace distance evolution
• On the Contractivity of Hilbert-Schmidt distance under open system dynamics

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