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SIC-POVMs: A new computer study
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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.
Forward citations
Cited by 3 Pith papers
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Optimal measures for p-frame energies on spheres
Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].
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A Constructive Approach to Zauner's Conjecture via the Stark Conjectures
A conditional proof that Zauner's SIC conjecture follows from the Stark conjectures plus a new 'Twisted Convolution' identity.
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Energy on spheres and discreteness of minimizing measures
For non-even p, every minimizer of the p-frame energy on the sphere has support with empty interior, and for potentials with finitely many positive Gegenbauer coefficients a discrete minimizer always exists.
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