The X²-divergence and mixing times of quantum Markov processes

Autor(en)

Kristan Paul Temme, Michael James Kastoryano, Mary Beth Ruskai, Michael M. Wolf, Frank Verstraete

Abstrakt

We introduce quantum versions of the χ2-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in the literature for classical Markov chains is taken to bound the trace-distance from the steady state of a quantum processes. A strict spectral bound to the convergence rate can be given for time-discrete as well as for time-continuous quantum Markov processes. Furthermore, the contractive behavior of the χ2-divergence under the action of a completely positive map is investigated and contrasted to the contraction of the trace norm. In this context we analyze different versions of quantum detailed balance and, finally, give a geometric conductance bound to the convergence rate for unital quantum Markov processes.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

University of Copenhagen, Tufts University, Max-Planck-Institut für Quantenoptik

Journal

Journal of Mathematical Physics

Band

51

Anzahl der Seiten

19

ISSN

0022-2488

DOI

https://doi.org/10.1063/1.3511335

Publikationsdatum

12-2010

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/057854f2-cff1-408f-aff8-31f56ef0b6b6