Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing

TL;DR

This paper develops a unified approach to optimal waveform estimation in classical and quantum systems using time-symmetric smoothing, with applications to quantum phase estimation and connections to weak value theory.

Contribution

It introduces a discrete-time framework for time-symmetric smoothing applicable to both classical and quantum systems, highlighting their similarities and extending quantum estimation techniques.

Findings

Unified classical and quantum smoothing framework

Application to quantum phase estimation with squeezed beams

Connection to weak value theory

Abstract

Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate waveforms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are emphasized. Application of the quantum theory to homodyne phase-locked loop design for phase estimation with narrowband squeezed optical beams is studied. The relation between the proposed theory and Aharonov et al.'s weak value theory is also explored.