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Published on: August 16, 2017
Entropic Bounds on Information Backflow
Nina Megier1, Andrea Smirne1, Bassano Vacchini1
1Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milan, Italy.
Abstract:
In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the trace-distance revivals between distinct evolved system states have been shown to be subordinated to the establishment of system-environment correlations or changes in the environmental state. We show that this interpretation can be substantiated also for a class of entropic quantifiers. We exploit a suitably regularized version of Umegaki's quantum relative entropy, known as telescopic relative entropy, that is tightly connected to the quantum Jensen-Shannon divergence. In particular, we derive general upper bounds on the telescopic relative entropy revivals conditioned and determined by the formation of correlations and changes in the environment. We illustrate our findings by means of examples, considering in particular the Jaynes-Cummings model and a phase covariant dynamics.
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