A smoothing theory for open quantum systems: The least mean square approach

TL;DR

This paper introduces a novel quantum smoothing theory based on least mean squared errors, addressing limitations of classical approaches by developing recursive equations for symmetric and skew parts of quantum estimates.

Contribution

It proposes a new quantum smoothing framework using least mean square errors, with recursive equations for symmetric and skew components, filling a gap in quantum estimation theory.

Findings

Developed recursive equations for quantum smoothing estimates.

Demonstrated the effectiveness of the least mean square approach in quantum systems.

Addressed the limitations of quantum conditional expectation in smoothing.

Abstract

Unlike the classical smoothing theory, it is well known that quantum smoothers are, in general, not well--defined by the quantum conditional expectation. The purpose of this paper is to propose a new quantum smoothing theory based on the least mean squared errors. The least mean square estimate of quantum physical quantity composes from symmetric part and skew part, and we developed the recursive equations, respectively.