Deviation bounds and concentration inequalities for quantum noises

Abstract

We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form. Introducing and developing new non-commutative functional inequalities, we deduce concentration inequalities for these processes. Examples satisfying our bounds include tensor products of quantum Markov semigroups as well as Gibbs samplers above a threshold temperature.

arXiv commentAccepted in Quantum, final version

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Cited by in corpus (4)

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• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Two-Time Measurement of Entropy Transfer in Markovian Quantum Dynamics