[quantum-info] PiQuDos seminar today - Alvaro Martin Alhambra

[Daniel Brod]

Reminder: Today at 4pm in the Time room, quantum information seminar by  Alvaro
Alhambra

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Title: Recovery maps in quantum thermodynamics


Abstract: A research line that has been very active recently in quantum
information is that of recoverability theorems. These, roughly speaking,
quantify how well can quantum information be restored 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.
On one hand, 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 reach thermal equilibrium.
On the other hand, we also show how the Petz recovery map appears in the
derivation of quantum fluctuation theorems, as the reversed work-extraction
process. From this fact alone, we show how a number of useful expressions
follow. These include a generalization of the majorization conditions that
includes fluctuating work, Crooks and Jarzynski's theorems, and an integral
fluctuation theorem that can be thought of as the second law as an equality.
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