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A First Course in the Sporadic SICs

  • Book
  • © 2021

Overview

Authors:
  1. Blake C. Stacey

    1. University of Massachusetts Boston, Boston, USA

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  • Includes significant advances in the study of SIC quantum measurements, also known as maximal sets of complex equiangular lines
  • Presents a comprehensive bibliography of SIC research
  • Provides exceedingly easy problem to state with great resistance to general solution

Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 41)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. Equiangular Lines

    • Blake C. Stacey
    Pages 1-11

  3. Optimal Quantum Measurements

    • Blake C. Stacey
    Pages 13-26

  4. Geometry and Information Theory for Qubits and Qutrits

    • Blake C. Stacey
    Pages 27-37

  5. SICs and Bell Inequalities

    • Blake C. Stacey
    Pages 39-55

  6. The Hoggar-Type SICs

    • Blake C. Stacey
    Pages 57-82

  7. Sporadic SICs and the Exceptional Lie Algebras

    • Blake C. Stacey
    Pages 83-101

  8. Exercises

    • Blake C. Stacey
    Pages 103-111

  9. Back Matter

    Pages 113-115
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Keywords

About this book

This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty.
While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.


Authors and Affiliations

  • University of Massachusetts Boston, Boston, USA

    Blake C. Stacey

About the author

Blake C. Stacey studied physics at MIT and Brandeis and currently researches quantum information theory at the University of Massachusetts Boston.

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