Stochastic heisenberg limit: optimal estimation of a fluctuating phase

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

doi:10.1103/PhysRevLett.111.113601

Stochastic heisenberg limit: optimal estimation of a fluctuating phase

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

^*Corresponding author for this work

Macquarie University Research Centre in Quantum Science and Technology

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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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.

Original language	English
Article number	113601
Pages (from-to)	1-5
Number of pages	5
Journal	Physical Review Letters
Volume	111
Issue number	11
DOIs	https://doi.org/10.1103/PhysRevLett.111.113601
Publication status	Published - 13 Sept 2013

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

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abstract = "The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cram{\'e}r-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.",

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Stochastic heisenberg limit: optimal estimation of a fluctuating phase

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