Time-symmetric quantum smoothing: A general theory of optimal quantum sensing

Mankei Tsang

The important problem of optimal waveform estimation for quantum sensing is solved using a time-symmetric approach. The theory generalizes prior work in classical and quantum estimation and can significantly out-perform previously proposed techniques.

Santiago Hernández-Gómez, Giovanni Fasiolo, Paola Cappellaro +2 more

V. P. Belavkin, Simon Edwards

Mankei Tsang

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.

Mankei Tsang

Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate wave forms 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 weak value theory of Aharonov et al. is also explored.