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A First Course in the Sporadic SICs

  • 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 SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 41)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Blake C. Stacey
    Pages 1-11
  3. Blake C. Stacey
    Pages 13-26
  4. Blake C. Stacey
    Pages 39-55
  5. Blake C. Stacey
    Pages 57-82
  6. Blake C. Stacey
    Pages 83-101
  7. Blake C. Stacey
    Pages 103-111
  8. Back Matter
    Pages 113-115

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.


Symmetric Informationally Complete Positive Operator Values Measure finite-dimensional Hilbert space Hoggar SIC Pauli operators Equiangular lines SIC-POVM

Authors and affiliations

  1. 1.University of Massachusetts BostonBostonUSA

About the authors

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

Bibliographic information