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Phys. Rev. A 75, 062101 (2007) [9 pages]

Parameter estimation for mixed states from a single copy

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Thomas Konrad1, Otfried Gühne2, Jürgen Audretsch3, and Hans J. Briegel2,4
1School of Physics, University of KwaZulu-Natal, Private Bag 54001, Durban 4000, South Africa
2Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, A-6020 Innsbruck, Austria
3Fachbereich Physik, Universität Konstanz, Fach M 674, D-78457 Konstanz, Germany
4Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria

Received 13 March 2007; published 1 June 2007

Given a single copy of a mixed state of the form ρ=λρ1+(1−λ)ρ2, what is the optimal measurement to estimate the parameter λ if ρ1 and ρ2 are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated value and the true value of λ. We explicitly determine the optimal measurements for a general two-dimensional system and for important higher dimensional cases.

© 2007 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.75.062101
DOI:
10.1103/PhysRevA.75.062101
PACS:
03.65.Wj, 03.67.−a, 03.65.Ta
 
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