Generalized repeated interaction model and transfer functions

TL;DR

This paper introduces a quantum repeated interaction model using lifting of row contractions, linking transfer functions with characteristic functions of liftings, and explores their properties in quantum systems.

Contribution

It presents a novel quantum interaction model with a transfer function framework, connecting multi-analytic operators and characteristic functions in a new way.

Findings

Transfer functions are multi-analytic operators.

Transfer functions are inner if the system is observable.

Transfer functions coincide with characteristic functions of liftings.

Abstract

Using a scheme involving a lifting of a row contraction we introduce a toy model of repeated interactions between quantum systems. In this model there is an outgoing Cuntz scattering system involving two wandering subspaces. We associate to this model an input/output linear system which leads to a transfer function. This transfer function is a multi-analytic operator, and we show that it is inner if we assume that the system is observable. Finally it is established that transfer functions coincide with characteristic functions of associated liftings.