Sinkhorn-Knopp theorem for PPT states

摘要

Given a PPT state A= n-ary sumation i=1nAi circle times Bi is an element of Mk circle times Mkdand a rank k tensor v within the image of A, we provide an algorithm that checks whether the positive map GA : Mk. Mk, GA( X) = n i= 1 tr ( Ai X) Bi, is equivalent to a doubly stochastic map. This procedure is based on the search for Perron eigenvectors of completely positive maps and unique solutions of, atmost, k unconstrained quadratic minimization problems. As a corollary, we can check whether this state can be put in the filter normal form. This normal form is an important tool for studying quantum entanglement. An extension of this procedure to PPT states in Mk. Mm is also presented.