Time-Symmetric Quantum Theory of Smoothing

TL;DR

This paper develops a quantum smoothing theory using a time-symmetric approach, enabling more accurate estimation of classical processes coupled to quantum systems with potential applications in quantum sensing technologies.

Contribution

It introduces a novel quantum smoothing framework that generalizes classical and quantum filtering, addressing the problem of optimal estimation in quantum measurement scenarios.

Findings

Provides a formalism for quantum smoothing using time symmetry

Improves estimation accuracy over filtering alone

Applicable to quantum sensing devices like gravitational wave detectors

Abstract

Smoothing is an estimation technique that takes into account both past and future observations, and can be more accurate than filtering alone. In this Letter, a quantum theory of smoothing is constructed using a time-symmetric formalism, thereby generalizing prior work on classical and quantum filtering, retrodiction, and smoothing. The proposed theory solves the important problem of optimally estimating classical Markov processes coupled to a quantum system under continuous measurements, and is thus expected to find major applications in future quantum sensing systems, such as gravitational wave detectors and atomic magnetometers.