Springer Theses

Formulation of Uncertainty Relation Between Error and Disturbance in Quantum Measurement by Using Quantum Estimation Theory

Authors: Watanabe, Yu

  • Formulates error and disturbance in quantum measurement in terms of Fisher information
  • Calculates the classical and quantum Fisher information using a Lie algebraic approach
  • Establishes in a groundbreaking work the fundamental bound on the accuracy of one measured observable and the disturbance on its conjugate one in the spirit of Heisenberg
  • Nominated as an outstanding contribution by the University of Tokyo's Physics Department in 2012
see more benefits

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-4-431-54493-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-4-431-54492-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 97,18 €
price for Spain (gross)
  • ISBN 978-4-431-56172-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

In this thesis, quantum estimation theory is applied to investigate uncertainty relations between error and disturbance in quantum measurement. The author argues that the best solution for clarifying the attainable bound of the error and disturbance is to invoke the estimation process from the measurement outcomes such as signals from a photodetector in a quantum optical system. The error and disturbance in terms of the Fisher information content have been successfully formulated and provide the upper bound of the accuracy of the estimation. Moreover, the attainable bound of the error and disturbance in quantum measurement has been derived.

The obtained bound is determined for the first time by the quantum fluctuations and correlation functions of the observables, which characterize the non-classical fluctuation of the observables. The result provides the upper bound of our knowledge obtained by quantum measurements.

The method developed in this thesis will be applied to a broad class of problems related to quantum measurement to build a next-generation clock standard and to successfully detect gravitational waves.

About the authors

Dr. Yu Watanabe
Kyoto University
Kitashirakawa Oiwake-Cho,
Sakyo-Ku, Kyoto
606-8502 Japan
yuwata@yukawa.kyoto-u.ac.jp

Table of contents (10 chapters)

  • Introduction

    Watanabe, Yu

    Pages 1-6

    Preview Buy Chapter 30,19 €
  • Reviews of Uncertainty Relations

    Watanabe, Yu

    Pages 7-17

    Preview Buy Chapter 30,19 €
  • Classical Estimation Theory

    Watanabe, Yu

    Pages 19-36

    Preview Buy Chapter 30,19 €
  • Quantum Estimation Theory

    Watanabe, Yu

    Pages 37-44

    Preview Buy Chapter 30,19 €
  • Expansion of Linear Operators by Generators of Lie Algebra $$\mathfrak {su}(d)$$ su ( d )

    Watanabe, Yu

    Pages 45-70

    Preview Buy Chapter 30,19 €

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-4-431-54493-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-4-431-54492-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 97,18 €
price for Spain (gross)
  • ISBN 978-4-431-56172-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Formulation of Uncertainty Relation Between Error and Disturbance in Quantum Measurement by Using Quantum Estimation Theory
Authors
Series Title
Springer Theses
Copyright
2014
Publisher
Springer Japan
Copyright Holder
Springer Japan
eBook ISBN
978-4-431-54493-7
DOI
10.1007/978-4-431-54493-7
Hardcover ISBN
978-4-431-54492-0
Softcover ISBN
978-4-431-56172-9
Series ISSN
2190-5053
Edition Number
1
Number of Pages
XIII, 122
Number of Illustrations and Tables
3 b/w illustrations, 5 illustrations in colour
Topics