Filtering of Wide Sense Stationary Quantum Stochastic Processes

TL;DR

This paper introduces a quantum analogue of wide sense stationary processes within a C*-algebra framework, defining their power spectrum and exploring linear quantum filters, bridging classical and quantum stochastic process theory.

Contribution

It presents the first formalization of quantum wide sense stationary processes, including their power spectrum and basic filtering methods, in a C*-algebra setting.

Findings

Defined quantum wide sense stationary processes in C*-algebras

Introduced the concept of power spectrum for these processes

Presented examples of linear quantum filters

Abstract

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on frequency space taking values in the expected algebra. The notion of linear quantum filters is introduced as some simple examples mentioned.