Finite Sample Analysis in Quantum Estimation

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Springer Science & Business Media, Jan 15, 2014 - Science - 118 pages

In this thesis, the author explains the background of problems in quantum estimation, the necessary conditions required for estimation precision benchmarks that are applicable and meaningful for evaluating data in quantum information experiments, and provides examples of such benchmarks.

The author develops mathematical methods in quantum estimation theory and analyzes the benchmarks in tests of Bell-type correlation and quantum tomography with those methods. Above all, a set of explicit formulae for evaluating the estimation precision in quantum tomography with finite data sets is derived, in contrast to the standard quantum estimation theory, which can deal only with infinite samples. This is the first result directly applicable to the evaluation of estimation errors in quantum tomography experiments, allowing experimentalists to guarantee estimation precision and verify quantitatively that their preparation is reliable.

 

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Contents

1 Introduction
1
Background and Problems in Quantum Estimation
7
Basic Concepts and Theoretical Tools for Finite Sample Analysis
12
4 Evaluation of Estimation Precision in Test of BellType Correlations
27
5 Evaluation of Estimation Precision in Quantum Tomography
37
6 Improvement of Estimation Precision by Adaptive Design of Experiments
89
7 Summary and Outlook
113
Curriculum Vitae
116
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About the author (2014)

Dr. Takanori Sugiyama Department of Physics, Graduate School of Science, The University of Tokyo

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