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Conference on Lasers and Electro-Optics

Time-Symmetric Quantum Smoothing: A General Theory of Optimal Quantum Sensing

Mankei Tsang

Published Jan 1, 2010• 0 citations
Publisher

Abstract

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.
DOI
10.1364/qels.2010.qthn7

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Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation. We consider both adaptive and nonadaptive quantum smoothing, and show that both are better than their filtered counterparts. For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2sqrt[2] times smaller than nonadaptive filtering (the standard quantum limit). The experimentally measured improvement is 2.24+/-0.14.

arXiv:0912.1162•Physical Review Letters•Mar 3, 2010•95 citations
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.
Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation. We consider both adaptive and nonadaptive quantum smoothing, and show that both are better than their filtered counterparts. For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2sqrt[2] times smaller than nonadaptive filtering (the standard quantum limit). The experimentally measured improvement is 2.24+/-0.14.