Finite Sample Analysis in Quantum Estimation

This book explains the background of problems in quantum estimation, the necessary conditions required for estimation precision benchmarks that are applicable for evaluating data in quantum information experiments, and examples of such benchmarks.

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.

Helps readers learn the basic concepts of quantum tomography by providing numerous step-by-step tutorials Includes a detailed description of how to choose estimation precision benchmarks Allows experimentalists to calculate the reliability of their estimation results with a developed finite sample theory Nominated as an outstanding contribution by the University of Tokyo's Physics Department in 2013 Includes supplementary material: sn.pub/extras

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

Inhalt
Introduction.- Quantum Mechanics and Quantum Estimation Background and Problems in Quantum Estimation.- Mathematical Statistics Basic Concepts and Theoretical Tools for Finite Sample Analysis.- Evaluation of Estimation Precision in Test of Bell-type Correlations.- Evaluation of Estimation Precision in Quantum Tomography.- Improvement of Estimation Precision by Adaptive Design of Experiments.- Summary and Outlook.