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Optimal pointers for joint measurement of σ(x) and σ(z) via homodyne detection

Janssens, Bas and Bouten, Luc (2006) Optimal pointers for joint measurement of σ(x) and σ(z) via homodyne detection. Journal of Physics A: Mathematical and General, 39 (11). pp. 2773-2790. ISSN 0305-4470. doi:10.1088/0305-4470/39/11/013.

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We study a model of a qubit in interaction with the electromagnetic field. By means of homodyne detection, the field-quadrature At + A*t is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred to the field, thus influencing the homodyne measurement results. We construct random variables (pointers) on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of σx and σz. Using variational calculus, we find the pointers that are optimal. These optimal pointers are very close to hitting the bound imposed by Heisenberg's uncertainty relation on joint measurement of two non-commuting observables. We close the paper by giving the probability densities of the pointers.

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Additional Information:© 2006 Institute of Physics and IOP Publishing Limited. Received 14 October 2005, in final form 18 January 2006. Published 1 March 2006. We thank Mădălin Guță and Hans Maassen for interesting discussions. We thank John Gough for a critical reading of the text. LB acknowledges support from the ARO under Grant DAAD19-03-1-0073.
Funding AgencyGrant Number
Army Research OfficeDAAD19-03-1-0073
Issue or Number:11
Record Number:CaltechAUTHORS:JANjpa06a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12501
Deposited By: Tony Diaz
Deposited On:23 Dec 2008 23:55
Last Modified:12 Jul 2022 19:45

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