论文标题
具有量子随机系统的二次指数力矩的概率边界
Probabilistic bounds with quadratic-exponential moments for quantum stochastic systems
论文作者
论文摘要
本文涉及二次指数矩（QEMS），用于具有位置摩托明群类型的量子随机系统的动态变量。 QEMs在尾巴概率分布上的量子动力学的统计``定位''对系统变量的正确定二次函数中起着重要作用。我们采用QEMS的随机表示，以系统变量的矩生成函数（MGF）来使用，该函数使用辅助经典的高斯随机向量在其参数上平均。该表示形式与MGF的加权$ l^2 $ norms结合在一起，从而导致系统变量的QEM上限。这些界限已证明具有真空输入场和非高斯初始状态的开放量子谐波振荡器。
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.
