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Optics and Spectroscopy

Studying adequacy, completeness, and accuracy of quantum measurement protocols

Yu. I. Bogdanov, I. D. Bukeev, A. K. Gavrichenko

Published Oct 1, 2011• 11 citations
Publisher

Abstract

A new methodology of statistical estimation of the quality of quantum measurement protocols is considered. The method is based on studying the completeness, adequacy, and accuracy of quantum measurement protocols. The completeness is estimated on the basis of considering a singular decomposition of a special matrix, which is constructed based on the measurement operators. The estimate of adequacy supposes the presence of redundancy in the measurement protocol as compared to the minimally possible number of measurements that are necessary for full reconstruction of a quantum state. The adequacy of quantum measurements is estimated as the degree of how much the redundant statistical data agree with the laws of quantum theory. The accuracy characteristics of the statistical reconstruction of arbitrary quantum states are studied based on the universal statistical distribution for accuracy losses. Examples of applying the developed methods are presented for seven quantum protocols based on the geometry of polyhedra with a high degree of symmetry.

DOI
10.1134/s0030400x11110038

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A new methodology of statistical estimation of the quality of quantum measurement protocols is considered. The method is based on studying the completeness, adequacy, and accuracy of quantum measurement protocols. The completeness is estimated on the basis of considering a singular decomposition of a special matrix, which is constructed based on the measurement operators. The estimate of adequacy supposes the presence of redundancy in the measurement protocol as compared to the minimally possible number of measurements that are necessary for full reconstruction of a quantum state. The adequacy of quantum measurements is estimated as the degree of how much the redundant statistical data agree with the laws of quantum theory. The accuracy characteristics of the statistical reconstruction of arbitrary quantum states are studied based on the universal statistical distribution for accuracy losses. Examples of applying the developed methods are presented for seven quantum protocols based on the geometry of polyhedra with a high degree of symmetry.
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