TY - JOUR

T1 - Universality of the Heisenberg limit for estimates of random phase shifts

AU - Hall, Michael J W

AU - Berry, Dominic W.

AU - Zwierz, Marcin

AU - Wiseman, Howard M.

N1 - 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

PY - 2012/4/13

Y1 - 2012/4/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84859999883&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.85.041802

DO - 10.1103/PhysRevA.85.041802

M3 - Article

AN - SCOPUS:84859999883

SN - 1050-2947

VL - 85

SP - 1

EP - 4

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 4

M1 - 041802

ER -