Time-Symmetric Quantum Theory of Smoothing

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.

4 pages, 1 figure, v2: accepted by PRL

References in corpus (3)

• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design
• Quantum theory of optical temporal phase and instantaneous frequency

Cited by in corpus (1)

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