Stochastic heisenberg limit: optimal estimation of a fluctuating phase

Dominic W. Berry, Michael J W Hall, Howard M. Wiseman

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramér-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as ω-p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N -2(p-1)/(p+1), where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p→∞) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.

LanguageEnglish
Article number113601
Pages1-5
Number of pages5
JournalPhysical Review Letters
Volume111
Issue number11
DOIs
Publication statusPublished - 13 Sep 2013

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Cramer-Rao bounds
estimating
statistics
scaling
photons
estimates

Bibliographical note

Berry, D. W., Hall, M. J. W., & Wiseman, H. M. (2013). Stochastic heisenberg limit : optimal estimation of a fluctuating phase. Physical review letters, 111(11), 113601, 2013. Copyright 2013 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.111.113601

Cite this

Berry, Dominic W. ; Hall, Michael J W ; Wiseman, Howard M. / Stochastic heisenberg limit : optimal estimation of a fluctuating phase. In: Physical Review Letters. 2013 ; Vol. 111, No. 11. pp. 1-5.
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Stochastic heisenberg limit : optimal estimation of a fluctuating phase. / Berry, Dominic W.; Hall, Michael J W; Wiseman, Howard M.

In: Physical Review Letters, Vol. 111, No. 11, 113601, 13.09.2013, p. 1-5.

Research output: Contribution to journalArticleResearchpeer-review

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