Wiener Filtering for Passive Linear Quantum Systems

TL;DR

This paper explores Wiener filtering for passive quantum linear systems, revealing unique quantum features and challenges such as nonconvex optimization and noise thresholds not present in classical equalization.

Contribution

It introduces a quantum-specific Wiener filtering framework and discusses relaxation approaches to solve the nonconvex optimization problem involved.

Findings

Quantum equalization involves nonconvex constrained optimization.

There exists a noise variance threshold for effective quantum equalization.

Quantum features lead to fundamentally different equalization challenges.

Abstract

This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically not encountered in classical equalization problems. Most significantly, finding a mean-square optimal quantum equalizing filter amounts to solving a nonconvex constrained optimization problem. We discuss two approaches to solving this problem, both involving a relaxation of the constraint. In both cases, unlike classical equalization, there is a threshold on the variance of the noise below which an improvement of the mean-square error cannot be guaranteed.