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}
}
  • Kun Fang, Hamza Fawzi
  • 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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 39 REFERENCES

    Quantum entanglement, sum of squares, and the log rank conjecture

    Weak Decoupling, Polynomial Folds and Approximate Optimization over the Sphere

    Classical deterministic complexity of Edmonds' Problem and quantum entanglement

    VIEW 1 EXCERPT