Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants

TL;DR

This paper addresses the design of a measurement-free quantum filter for linear quantum systems, aiming to minimize the difference between the system's variables and the filter output, using covariance control techniques.

Contribution

It introduces a coherent quantum filtering approach for physically realizable linear quantum plants, transforming the problem into a constrained covariance control problem.

Findings

Formulation of CQF as a covariance control problem

Use of Frechet differentiation for filter matrix optimization

Simplified feedback-free quantum filtering solution

Abstract

The paper is concerned with a problem of coherent (measurement-free) filtering for physically realizable (PR) linear quantum plants. The state variables of such systems satisfy canonical commutation relations and are governed by linear quantum stochastic differential equations, dynamically equivalent to those of an open quantum harmonic oscillator. The problem is to design another PR quantum system, connected unilaterally to the output of the plant and playing the role of a quantum filter, so as to minimize a mean square discrepancy between the dynamic variables of the plant and the output of the filter. This coherent quantum filtering (CQF) formulation is a simplified feedback-free version of the coherent quantum LQG control problem which remains open despite recent studies. The CQF problem is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.