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Quantum Simulation Entanglement Theory Quantum Correlations

Geometric properties of SIC-POVM tensor square

arXiv
Authors: Vasyl Ostrovskyi, Danylo Yakymenko

Year

2019

Paper ID

14838

Status

Preprint

Abstract Read

~2 min

Abstract Words

132

Citations

N/A

Abstract

It's known that if d2 vectors from d-dimensional Hilbert space H form a SIC-POVM (SIC for short) then tensor square of those vectors form an equiangular tight frame on the symmetric subspace of Hotimes H. We prove that for any SIC of WH-type (Weyl-Heisenberg group covariant) this squared frame can be obtained as a projection of WH-type basis of Hotimes H onto the symmetric subspace. We give a full description of the set of all WH-type bases, so this set could be used as a search space for SIC solutions. Also we show that a particular element of this set is close to a SIC solution in some structural sense. Finally we give a geometric construction of a SIC-related symmetric tight fusion frames that were discovered in odd dimensions.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • It's known that if d^2 vectors from d-dimensional Hilbert space H form a SIC-POVM (SIC for short) then tensor square of those vectors form an equiangular tight frame on the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1911.05437 [2] arXiv https://arxiv.org/abs/1911.05437 [3] Publisher https://arxiv.org/abs/1911.05437

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