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arXiv · 1111.0788

Universality of the Heisenberg limit for estimates of random phase shifts

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

The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/ , where 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. Our result gives the first completely general, constraint-free and non-asymptotic 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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Michael J. W. Hall, Dominic W. Berry, Marcin Zwierz, Howard M. Wiseman. 2012-04-18. Universality of the Heisenberg limit for estimates of random phase shifts. https://doi.org/10.1103/physreva.85.041802

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