Universality of the Heisenberg limit for estimates of random phase shifts

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Title Universality of the Heisenberg limit for estimates of random phase shifts
Author Hall, Michael; Berry, Dominic W.; Zwierz, Marcin; Wiseman, Howard Mark
Journal Name Physical Review A
Year Published 2012
Place of publication United States
Publisher American Physical Society
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.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1103/PhysRevA.85.041802
Copyright Statement Copyright 2012 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 85
Page from 041802-1
Page to 041802-4
ISSN 1050-2947
Date Accessioned 2012-05-28
Language en_US
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Quantum Information, Computation and Communication
URI http://hdl.handle.net/10072/46962
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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