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.

Accepted in Quantum, final version

References in corpus (6)

• Hypercontractivity of quasi-free quantum semigroups
• Complete entropic inequalities for quantum Markov chains
• Sanov and Central Limit Theorems for output statistics of quantum Markov chains
• Quantum concentration inequalities
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Ricci curvature of quantum channels on non-commutative transportation metric spaces

Cited by in corpus (4)

• Fundamental bounds on precision and response for quantum trajectory observables
• 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