Entropy production of doubly stochastic quantum channels
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We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
Originalsprog | Engelsk |
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Artikelnummer | 022203 |
Tidsskrift | Journal of Mathematical Physics |
Vol/bind | 57 |
Udgave nummer | 2 |
ISSN | 0022-2488 |
DOI | |
Status | Udgivet - 1 feb. 2016 |
ID: 232254551