Probabilistic bounds with quadratic-exponential moments for quantum stochastic systems

• URL: http://arxiv.org/abs/2211.12161v1
• Date: Tue, 22 Nov 2022 10:40:52 GMT
• Title: Probabilistic bounds with quadratic-exponential moments for quantum stochastic systems
• Authors: Igor G. Vladimirov
• Abstract summary: quadratic-exponential moments (QEMs) for dynamic variables of quantum systems with position-momentum type canonical commutation relations. QEMs play an important role for statistical localisation'' of the quantum dynamics in the form of upper bounds on the tail probability distribution for a positive definite function of the system variables.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical ``localisation'' of the quantum dynamics in the form of upper bounds on the tail probability distribution for a positive definite quadratic function of the system variables. We employ a randomised representation of the QEMs in terms of the moment-generating function (MGF) of the system variables, which is averaged over its parameters using an auxiliary classical Gaussian random vector. This representation is combined with a family of weighted $L^2$-norms of the MGF, leading to upper bounds for the QEMs of the system variables. These bounds are demonstrated for open quantum harmonic oscillators with vacuum input fields and non-Gaussian initial states.

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