Universality of the Heisenberg limit for estimates of random phase shifts

Details Universality of the Heisenberg limit for estimates of random phase shifts Universality of the Heisenberg limit for estimates of random phase shifts

2011-11-03

arxiv.org/abs/1111.0788v3

Phys. Rev. A 85, 041802(R) (2012)

Physics

Quantum Physics

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Scientific paper

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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