Adaptive optical phase estimation using time-symmetric quantum smoothing

T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Furusawa, E. H. Huntington

Research output: Contribution to journalArticlepeer-review

88 Citations (Scopus)


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 2√2 times smaller than nonadaptive filtering (the standard quantum limit). The experimentally measured improvement is 2.24±0.14.

Original languageEnglish
Article number093601
Pages (from-to)1-4
Number of pages4
JournalPhysical Review Letters
Issue number9
Publication statusPublished - 3 Mar 2010
Externally publishedYes


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