The χ2-divergence and mixing times of quantum Markov processes
By Kristan Temme, Michael J. Kastoryano, Mary Beth Ruskai, Michael M. Wolf, Frank Verstraete. 2010
179 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/3e719c8550cd7808129d6bdd1bec757b06097e91
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Quantum logarithmic Sobolev inequalities and rapid mixing (2012, background): “However, it can be seen that λ can always be understood as the second largest eigenvalue of an appropr iately weighted symmetrization [18].”