Universality of the Heisenberg limit for estimates of random phase shifts

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

doi:10.1103/PhysRevA.85.041802

Universality of the Heisenberg limit for estimates of random phase shifts

Michael J W Hall^*, Dominic W. Berry, Marcin Zwierz, 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

69 Citations (Scopus)

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Abstract

The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/N, where N is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts, applicable to any estimate of a completely unknown phase shift. Our result gives a completely general, constraint-free, and nonasymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including multiple passes, nonlinear phase shifts, multimode probes, and arbitrary measurements.

Original language	English
Article number	041802
Pages (from-to)	1-4
Number of pages	4
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	85
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevA.85.041802
Publication status	Published - 13 Apr 2012

Bibliographical note

Hall, MJW, Berry, DW, Zwierz, M. and Wiseman, HM. Physical review A. Atomic, molecular, and optical physics, 85(4), 041802(R), 2012. Copyright (2012) by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevA.85.041802

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abstract = "The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/N, where N is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts, applicable to any estimate of a completely unknown phase shift. Our result gives a completely general, constraint-free, and nonasymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including multiple passes, nonlinear phase shifts, multimode probes, and arbitrary measurements.",

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Universality of the Heisenberg limit for estimates of random phase shifts

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