Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information

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Title Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
Author Hall, Michael; Wiseman, Howard Mark
Journal Name New Journal of Physics
Year Published 2012
Place of publication United Kingdom
Publisher IOP Publishing Ltd
Abstract A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form kI/〈2|G|〉 where G is the generator of the shift (with an arbitrary discrete or continuous spectrum), and hence establishes a universally applicable bound of the same form as the usual Heisenberg limit. The scaling constant kI depends on prior information about the shift parameter. For example, in phase sensing regimes, where the phase shift is confined to some small interval of length L, the relative resolution has the strict lower bound (2πe3)−1/2/〈2m|G1| + 1〉, where m is the number of probes, each with generator G1, and entangling joint measurements are permitted. Generalizations using other resource measures and including noise are briefly discussed. The results rely on the derivation of general entropic uncertainty relations for continuous observables, which are of interest in their own right.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1088/1367-2630/14/3/033040
Copyright Statement Copyright 2012 Institute of Physics Publishing. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 14
Page from 033040-1
Page to 033040-22
ISSN 1367-2630
Date Accessioned 2012-05-28
Language en_US
Comments Page numbers are not for citation purposes. Instead, this article has the unique article number of 033040.
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/10072/46992
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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