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Axioms 2017, 6(3), 21; doi:10.3390/axioms6030021

The SIC Question: History and State of Play

1
Physics Department, University of Massachusetts Boston, Boston, MA 02125, USA
2
Computer Science Department, University of Massachusetts Boston, Boston, MA 02125, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Palle Jorgensen
Received: 30 June 2017 / Revised: 14 July 2017 / Accepted: 15 July 2017 / Published: 18 July 2017
(This article belongs to the Special Issue Wavelet and Frame Constructions, with Applications)
View Full-Text   |   Download PDF [344 KB, uploaded 24 July 2017]   |  

Abstract

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott’s code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research. View Full-Text
Keywords: quantum information; quantum measurement; SIC-POVM; equiangular lines; Weyl–Heisenberg group quantum information; quantum measurement; SIC-POVM; equiangular lines; Weyl–Heisenberg group
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Fuchs, C.A.; Hoang, M.C.; Stacey, B.C. The SIC Question: History and State of Play. Axioms 2017, 6, 21.

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