skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Minimal sufficient positive-operator valued measure on a separable Hilbert space

Abstract

We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.

Authors:
 [1]
  1. Department of Nuclear Engineering, Kyoto University, 6158540 Kyoto (Japan)
Publication Date:
OSTI Identifier:
22479542
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FUZZY LOGIC; HILBERT SPACE; QUANTUM SYSTEMS; STATISTICS

Citation Formats

Kuramochi, Yui. Minimal sufficient positive-operator valued measure on a separable Hilbert space. United States: N. p., 2015. Web. doi:10.1063/1.4934235.
Kuramochi, Yui. Minimal sufficient positive-operator valued measure on a separable Hilbert space. United States. https://doi.org/10.1063/1.4934235
Kuramochi, Yui. 2015. "Minimal sufficient positive-operator valued measure on a separable Hilbert space". United States. https://doi.org/10.1063/1.4934235.
@article{osti_22479542,
title = {Minimal sufficient positive-operator valued measure on a separable Hilbert space},
author = {Kuramochi, Yui},
abstractNote = {We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.},
doi = {10.1063/1.4934235},
url = {https://www.osti.gov/biblio/22479542}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 10,
volume = 56,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2015},
month = {Thu Oct 15 00:00:00 EDT 2015}
}