# Geometric properties of SIC-POVM tensor square

@article{Ostrovskyi2019GeometricPO,
title={Geometric properties of SIC-POVM tensor square},
author={Vasyl Ostrovskyi and Danylo Yakymenko},
journal={Letters in Mathematical Physics},
year={2019},
volume={112},
pages={1-27}
}
• Published 13 November 2019
• Mathematics
• Letters in Mathematical Physics
It is known that if $$d^2$$ d 2 vectors in a d -dimensional Hilbert space H form a symmetric, informationally complete, positive operator-valued measure (SIC-POVM), then the tensor squares of these vectors form an equiangular tight frame in the symmetric subspace of $$H\otimes H$$ H ⊗ H . We prove that, for any SIC-POVM of the Weyl–Heisenberg group covariant type (WH-type), this frame can be obtained by projecting a WH-type basis in $$H\otimes H$$ H ⊗ H onto the symmetric subspace. We give a…
• Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2022
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