Finite Sample Analysis in Quantum Estimation

✍ Scribed by Takanori Sugiyama (auth.)

• Publisher: Springer Japan
• Year: 2014
• Tongue: English
• Leaves: 125
• Series: Springer Theses
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-5
Quantum Mechanics and Quantum Estimation: Background and Problems in Quantum Estimation....Pages 7-11
Mathematical Statistics: Basic Concepts and Theoretical Tools for Finite Sample Analysis....Pages 13-26
Evaluation of Estimation Precision in Test of Bell-Type Correlations....Pages 27-36
Evaluation of Estimation Precision in Quantum Tomography....Pages 37-87
Improvement of Estimation Precision by Adaptive Design of Experiments....Pages 89-112
Summary and Outlook....Pages 113-115
Back Matter....Pages 117-118

✦ Subjects

Quantum Physics; Quantum Information Technology, Spintronics; Quantum Optics; Measurement Science and Instrumentation; Data Structures, Cryptology and Information Theory