Convex decompositions of Q-stochastic tensors and Bell locality in a multipartite system

Abstract

Generalizing the notions of the row and the column stochastic matrices, we introduce the multidimensional Q-stochastic tensors. We prove that every Q-stochastic tensor can be decomposed as a convex combination of finitely many binary Q-stochastic tensors and that the binary Q-stochastic tensors are exactly the extreme points of the compact convex set of all Q-stochastic tensors with the same size. Applications to characterizing the Bell locality of a quantum state in a multipartite system are demonstrated. Algorithms for computing the convex decompositions of Q-stochastic tensors are provided.