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Article Dans Une Revue Quantum Année : 2022

Deviation bounds and concentration inequalities for quantum noises

Résumé

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.
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Dates et versions

hal-03356802 , version 1 (08-01-2024)

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Tristan Benoist, Lisa Hänggli, Cambyse Rouzé. Deviation bounds and concentration inequalities for quantum noises. Quantum, 2022, ⟨10.22331/q-2022-08-04-772⟩. ⟨hal-03356802⟩
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