# The SIC Question: History and State of Play

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## Abstract

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## 1. Introduction

## 2. Generating SICs with Groups

## 3. Historical Overview

## 4. How to Search for SICs Numerically

## 5. Zauner Symmetry

## 6. Exhaustive Searches

## 7. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Topic | References |
---|---|

Abstract algebra | [8,10,11,71] |

Algebraic number theory | [5,6,7,26,62,72] |

Category theory | [73,74] |

Compressed sensing and signal processing | [75,76,77,78] |

Elliptic curves | [41,50,79,80] |

Exact solutions | [4,8,25,26,81,82,83,84,85,86] |

Frame theory | [25,37,63,77,78,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101] |

Finite group theory | [9,12,13,21,47,101,102,103,104,105,106,107] |

Generalized and approximate SICs | [71,74,108,109,110,111,112,113,114,115,116] |

Historical overview | [45,117,118] |

Informational power and entropy | [13,21,53,119,120,121,122,123,124,125,126,127,128,129] |

Laboratory experiments | [28,29,30,31,32,33,34,35] |

Multipartite systems and sequential measurements | [47,83,130,131,132,133,134,135,136] |

Quantum communication and cryptography | [28,29,137,138,139,140,141,142,143] |

Quantum computing and contextuality | [13,20,40,53,135,144,145,146,147,148,149,150,151] |

Quantum decoherence | [152,153] |

Quantum entanglement | [19,112,113,114,137,139,154] |

Quantum tomography | [18,31,36,63,71,133,134,138,140,155,156,157,158,159,160,161,162,163,164,165] |

Quaternions and octonions | [9,13,48,49,73,166,167] |

Reconstructing quantum theory | [14,17,22,23,40,74,117,135,168,169,170,171,172] |

SICs and Mutually Unbiased Bases | [16,53,80,125,145,151,173,174,175,176,177,178,179,180,181,182,183,184,185,186] |

SICs, Wigner functions and phase space representations | [20,29,40,53,83,89,90,144,174,187,188,189,190] |

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## Share and Cite

**MDPI and ACS Style**

Fuchs, C.A.; Hoang, M.C.; Stacey, B.C.
The SIC Question: History and State of Play. *Axioms* **2017**, *6*, 21.
https://doi.org/10.3390/axioms6030021

**AMA Style**

Fuchs CA, Hoang MC, Stacey BC.
The SIC Question: History and State of Play. *Axioms*. 2017; 6(3):21.
https://doi.org/10.3390/axioms6030021

**Chicago/Turabian Style**

Fuchs, Christopher A., Michael C. Hoang, and Blake C. Stacey.
2017. "The SIC Question: History and State of Play" *Axioms* 6, no. 3: 21.
https://doi.org/10.3390/axioms6030021