17 citations · 52 across the 24 of their papers we have counts for
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math.OC2017
A lower bound on the positive semidefinite rank of convex bodies
Hamza Fawzi, Mohab Safey El Din
The positive semidefinite rank of a convex body is the size of its smallest positive semidefinite formulation. We show that the positive semidefinite rank of any convex body $C…
quant-ph2017
Efficient optimization of the quantum relative entropy
Hamza Fawzi, Omar Fawzi
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a s…
math.OC2017
Semidefinite approximations of the matrix logarithm
Hamza Fawzi, James Saunderson, Pablo A. Parrilo
The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to nu…