# The sum-of-squares hierarchy on the sphere and applications in quantum information theory

@article{Fang2019TheSH,
title={The sum-of-squares hierarchy on the sphere and applications in quantum information theory},
author={Kun Fang and Hamza Fawzi},
journal={Mathematical Programming},
year={2019},
pages={1-30}
}
• Published 2019
• Mathematics, Computer Science, Physics
• Mathematical Programming
• We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique , we obtain a quadratic improvement of the known convergence rate by Reznick and Doherty and Wehner. Specifically, we show that the rate of convergence is no worse than $$O(d^2/\ell ^2)$$ O ( d 2 / ℓ 2 ) in the regime $$\ell = \Omega (d)$$ ℓ = Ω ( d ) where $$\ell$$ ℓ is the level of the hierarchy and d the dimension… CONTINUE READING

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