H
Hamza Fawzi
Researcher at University of Cambridge
Publications - 69
Citations - 2469
Hamza Fawzi is an academic researcher from University of Cambridge. The author has contributed to research in topics: Semidefinite programming & Positive-definite matrix. The author has an hindex of 17, co-authored 59 publications receiving 1997 citations. Previous affiliations of Hamza Fawzi include University of California, Los Angeles & Massachusetts Institute of Technology.
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Sparse sum-of-squares certificates on finite abelian groups
TL;DR: In this paper, the Cayley graph Cay($\hat{G,S}) with maximal cliques related to the Fourier basis is constructed, and it is shown that any nonnegative quadratic form in n binary variables is a sum of squares of functions of degree at most Ω(n/2 \rceil), where n is the number of vertices.
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Equivariant semidefinite lifts and sum-of-squares hierarchies
TL;DR: In this paper, it was shown that any equivariant psd lift of size d of an orbitope is of sum-of-squares type, where the functions in the sum of squares decomposition come from an invariant subspace of dimension smaller than d^3.
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A lower bound on the positive semidefinite rank of convex bodies
Hamza Fawzi,Mohab Safey El Din +1 more
TL;DR: It is shown that the positive semidefinite rank of any convex body $C$ is at least $\sqrt{\log d}$, where $d$ is the smallest degree of a polynomial that vanishes on the boundary of the polar of $C$.
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Relative entropy optimization in quantum information theory via semidefinite programming approximations
Hamza Fawzi,Omar Fawzi +1 more
TL;DR: This work uses the approximation method proposed in [Fawzi, Saunderson, Parrilo, Semidefinite approximations of the matrix logarithm, arXiv:1705.00812] to provide numerical counterexamples for a proposed lower bound on the quantum conditional mutual information in terms of the relative entropy of recovery.
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Rational and real positive semidefinite rank can be different
TL;DR: In this paper, the rational-restricted psd rank is shown to be always an upper bound to the usual pd rank, where the matrix factors are required to be rational symmetric psd matrices.