Annals of Physics
Volume 311, Issue 1
doi:10.1016/j.aop.2003.12.002 Cite or link using doi
Copyright © 2003 Elsevier Inc. All rights reserved.
Strategies to measure a quantum state
Franz Embacher , and Heide Narnhofer
Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, A-1090, Wien, Austria
Received 30 October 2003. Available online 24 December 2003.
We consider the problem of determining the mixed
quantum state of a large but finite number of identically prepared
quantum systems from data obtained in a sequence of ideal (von Neumann)
measurements, each performed on an individual copy of the system. In
contrast to previous approaches, we do not average over the possible
unknown states but work out a "typical" probability distribution on the
set of states, as implied by the experimental data. As a consequence,
any measure of knowledge about the unknown state and thus any notion of
"best strategy" (i.e., the choice of observables to be measured, and
the number of times they are measured) depend on the unknown state. By
learning from previously obtained data, the experimentalist re-adjusts
the observable to be measured in the next step, eventually approaching
an optimal strategy. We consider two measures of knowledge and exhibit
all "best" strategies for the case of a two-dimensional Hilbert space.
Finally, we discuss some features of the problem in higher dimensions
and in the infinite dimensional case.
Corresponding author. Fax: +4342779515
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