Quantum stochastic processes

Stochastic Processes and Quantum Mechanics

5 Reconstruction Theorem for Quantum Stochastic Processes

Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered field in an arbitrary space–time region T of an open quantum system under a sequential observation at a discrete space-time localization. It is shown that to every QSP described in the weak sense by a self-consistent system of causally ordered correlation kernels there correspo...

Quantum Recurrent Networks for Simulating Stochastic Processes

We introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks. We show that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties finding application in pattern recognition, optimization and simulation. Moreover, decoherence in qu...

Positive Definite Germs of Quantum Stochastic Processes

A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Itô algebra. A representation theorem, giving the pseudo-Hilbert dilation for the germ-matrix of the differential, is proved. This suggests the general form of quantum stochastic evolution ...

Exotic Stochastic Processes from Complex Quantum Environments

Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle coupled to such environments displays a variety of stochastic behaviors, ranging from turbulent diffusion to Lévy processes and Brownian motion. Dissipation and ...