Quantifying the evolution of mixed quantum states

Abstract We present a measure of quantum evolution based on the degree of average distinguishability between the states visited by a quantum system over a given time interval. This measure generalizes the concept of ‘amount of evolution’ previously introduced for pure states, to arbitrary (mixed) states, thereby enabling the study of non-unitary dynamics in open quantum systems. For qubit systems, we establish fundamental relationships between the proposed evolution measure and state purity, deriving rigorous bounds for the evolution quantity. Furthermore, we demonstrate that the proposed measure admits a natural interpretation in terms of the entanglement between the system and a purifying environment, in such a way that the evolution measure globally reflects the degree of variation of the system-environment entanglement. Finally, we illustrate the behavior of the evolution measure in qubit systems interacting with an environment under paradigmatic decoherence dynamics.