NDLI: Lower Bounds for Quantum Parameter Estimation

Content Provider	IEEE Xplore Digital Library
Author	Walter, M. Renes, J.M.
Copyright Year	1963
Abstract	The laws of quantum mechanics place fundamental limits on the accuracy of measurements and, therefore, on the estimation of unknown parameters of a quantum system. In this paper, we prove lower bounds on the size of confidence regions reported by any region estimator for a given ensemble of probe states and probability of success. Our bounds are derived from a previously unnoticed connection between the size of confidence regions and the error probabilities of a corresponding binary hypothesis test. In group-covariant scenarios, we find that there is an ultimate bound for any estimation scheme, which depends only on the representation-theoretic data of the probe system, and we evaluate its asymptotics in the limit of many systems, establishing a general Heisenberg limit for region estimation. We apply our results to several examples, in particular, to phase estimation, where our bounds allow us to recover the well-known Heisenberg and shot-noise scaling.
Sponsorship	IEEE Information Theory Society
Starting Page	8007
Ending Page	8023
Page Count	17
File Size	563148
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Probes Entropy Quantum mechanics Estimation Mean square error methods Parameter estimation Testing representation theory Quantum parameter estimation confidence regions lower bounds Heisenberg limit covariant estimation hypothesis testing quantum information theory
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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