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Title: Quantum chi-squared and goodness of fit testing

A quantum mechanical hypothesis test is presented for the hypothesis that a certain setup produces a given quantum state. Although the classical and the quantum problems are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. A goodness of fit test for i.i.d quantum states is developed and a max-min characterization for the optimal measurement is introduced. We find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiencies, and determine the associated divergence rates. We discuss the relationship of the quantum goodness of fit test to the problem of estimating multiple parameters from a density matrix. These problems are found to be closely related and we show that the largest error of an optimal strategy, determined by the smallest eigenvalue of the Fisher information matrix, is given by the divergence rate of the goodness of fit test.
Authors:
 [1] ;  [2]
  1. IQIM, California Institute of Technology, Pasadena, California 91125 (United States)
  2. Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria and Faculty of Science, Ghent University, B-9000 Ghent (Belgium)
Publication Date:
OSTI Identifier:
22403085
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; EIGENVALUES; HYPOTHESIS; QUANTUM MECHANICS; QUANTUM STATES; TESTING