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

Research output: Contribution to journalArticle

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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 languageEnglish
Article number041802
Pages (from-to)1-4
Number of pages4
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume85
Issue number4
DOIs
Publication statusPublished - 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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