Quantum chi-squared and goodness of fit testing

Autor(en)

Kristan Temme, Frank Verstraete

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University , California Institute of Technology (Caltech)

Journal

Journal of Mathematical Physics

Band

56

Anzahl der Seiten

18

ISSN

0022-2488

DOI

https://doi.org/10.1063/1.4905843

Publikationsdatum

01-2015

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/1f347731-d706-483a-8cc8-55923566b517