A conditional proof that Zauner's SIC conjecture follows from the Stark conjectures plus a new 'Twisted Convolution' identity.
SIC-POVMs: A new computer study
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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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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.