Bipartite Matrix-Valued Tensor Product Correlations That are Not Finitely Representable

Abstract

We consider the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. These sets are denoted by \(C_q^{(n)}(m,k)\) and \(C_{qs}^{(n)}(m,k)\), respectively, where m is the number of inputs, k is the number of outputs, and n is the matrix size. We show that, for any \(m,k \ge 2\) with \((m,k) \ne (2,2)\), there is an \(n \le 4\) for which we have the separation \(C_q^{(n)}(m,k) \ne C_{qs}^{(n)}(m,k)\).