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Recovery maps in quantum thermodynamics

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One of the most active research lines in recent times in quantum information has been that of recoverability theorems. These, roughly speaking, quantify how well quantum information can be recovered after some general CPTP map, through particular recovery maps. In this talk, I will outline what this line of work can teach us about quantum thermodynamics, and about the irreversibility of thermalization processes.

The recovery map is associated with how well one can recover a state after a quantum evolution and we show that the dynamical semigroups describing thermalization, namely Davies maps, have the curious property of being their own recovery map, as a consequence of a condition named quantum detailed balance. For these maps, we derive a tight bound relating the entropy production at time t with the state of the system at time 2t, which puts a strong constraint on how systems thermalize. I will also outline how the Petz recovery map appears in the derivation of quantum fluctuation theorems, as the reversed work-extraction process. These results give definite examples of intriguing connections between informational and physical reversibility.

This talk is part of the CQIF Seminar series.

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