124 citations · 361 across the 23 of their papers we have counts for
4 papers · 1 filter
The phase rank of a matrix
António Pedro Goucha, João Gouveia
In this paper, we introduce and study the notion of phase rank. Given a matrix filled with phases, i.e., with complex entries of modulus , its phase rank is the smallest possibl…
Complex psd-minimal polytopes in dimensions two and three
Tristram Bogart, João Gouveia, Juan Camilo Torres
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real se…
General non-realizability certificates for spheres with linear programming
Joao Gouveia, Antonio Macchia, Amy Wiebe
In this paper we present a simple technique to derive certificates of non-realizability for an abstract polytopal sphere. Our approach uses a variant of the classical algebraic cer…
Quantum marginals, faces, and coatoms
Stephan Weis, João Gouveia
Many problems of quantum information theory rely on the set of quantum marginals. A precise knowledge of the faces of this convex set is necessary, for example, in the reconstructi…