@inproceedings{1f9d78bcfeb54dbd984887ee68a40fc7,
title = "Probabilistic Bounds with Quadratic-Exponential Moments for Quantum Stochastic Systems",
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 L2-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.",
keywords = "moment-generating function, probabilistic bound, Quadratic-exponential moment, quantum stochastic system, randomised representation",
author = "Vladimirov, \{Igor G.\}",
note = "Publisher Copyright: Copyright {\textcopyright} 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",
year = "2023",
month = jul,
day = "1",
doi = "10.1016/j.ifacol.2023.10.113",
language = "English",
series = "IFAC-PapersOnLine",
publisher = "Elsevier B.V.",
number = "2",
pages = "5185--5190",
editor = "Hideaki Ishii and Yoshio Ebihara and Jun-ichi Imura and Masaki Yamakita",
booktitle = "IFAC-PapersOnLine",
address = "Netherlands",
edition = "2",
}