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Finite Sample Analysis in Quantum Estimation

  • Takanori Sugiyama

Part of the Springer Theses book series (Springer Theses)

Table of contents

About this book

Introduction

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.

Keywords

Finite Sample Analysis Quantum Estimation Theory Quantum Information Quantum Tomography Statistical Error Analysis Test of Bell-type Correlation

Authors and affiliations

  • Takanori Sugiyama
    • 1
  1. 1.Department of Physics Graduate School of ScienceThe University of TokyoTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-54777-8
  • Copyright Information Springer Japan 2014
  • Publisher Name Springer, Tokyo
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-4-431-54776-1
  • Online ISBN 978-4-431-54777-8
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
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