Entropy production of doubly stochastic quantum channels
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Entropy production of doubly stochastic quantum channels. / Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.
I: Journal of Mathematical Physics, Bind 57, Nr. 2, 022203, 01.02.2016.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Entropy production of doubly stochastic quantum channels
AU - Müller-Hermes, Alexander
AU - Stilck França, Daniel
AU - Wolf, Michael M.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - 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.
AB - 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.
U2 - 10.1063/1.4941136
DO - 10.1063/1.4941136
M3 - Journal article
VL - 57
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 2
M1 - 022203
ER -
ID: 232254551