A homomorphism theorem and a Trotter product formula for quantum stochastic flows with unbounded coefficients

TL;DR

This paper introduces a novel method to establish the homomorphic property of quantum stochastic flows with unbounded coefficients and applies it to derive a Trotter product formula and quantum stochastic dilations, extending existing results.

Contribution

It presents a new approach for proving homomorphism in quantum stochastic flows with unbounded coefficients and generalizes quantum dynamical semigroup dilations.

Findings

Proved homomorphic property for quantum stochastic flows with unbounded coefficients.

Established a Trotter product formula for quantum stochastic flows.

Obtained quantum stochastic dilations of a broader class of quantum dynamical semigroups.

Abstract

We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5]