432 citations · 1k across the 5 of their papers we have counts for
7 papers
Detecting multipartite entanglement
Andrew C. Doherty, Pablo A. Parrilo, Federico M. Spedalieri
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for ch…
A complete family of separability criteria
Andrew C. Doherty, Pablo A. Parrilo, Federico M. Spedalieri
We introduce a new family of separability criteria that are based on the existence of extensions of a bipartite quantum state to a larger number of parties satisfying certain s…
The Lax conjecture is true
Adrian S. Lewis, Pablo A. Parrilo, Motakuri V. Ramana
In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recen…
Symmetry groups, semidefinite programs, and sums of squares
Karin Gatermann, Pablo A. Parrilo
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic,…
A geometric inequality for circle packings
Pablo A. Parrilo, Ronen Peretz
A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity o…
Distinguishing separable and entangled states
Andrew C. Doherty, Pablo A. Parrilo, Federico M. Spedalieri
We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Hor…