SIC-POVMs: A new computer study
A. J. Scott, M. Grassl
TL;DR
This paper presents a comprehensive computational study of SIC-POVMs, exploring their existence in various dimensions and providing new algebraic solutions, advancing understanding in quantum measurement theory.
Contribution
It offers the first extensive numerical and algebraic investigation of SIC-POVMs across multiple dimensions, including new solutions and symmetry analyses.
Findings
Numerical solutions for all dimensions d <= 67
Complete list of Weyl-Heisenberg covariant solutions for d <= 50
New algebraic solutions in dimensions 24, 35, and 48
Abstract
We report on a new computer study into the existence of d^2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the underlying mathematical objects defining symmetric informationally complete measurements in quantum theory. We provide numerical solutions in all dimensions d <= 67 and, moreover, a putatively complete list of Weyl-Heisenberg covariant solutions for d <= 50. A symmetry analysis of this list leads to new algebraic solutions in dimensions d = 24, 35 and 48, which are given together with algebraic solutions for d = 4,..., 15 and 19.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Algebra and Geometry · Algebraic structures and combinatorial models