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 ≥ 2 with (m,k) ≠ (2,2), there is an n ≤ 4 for which we have the separation C_q⁽ⁿ⁾(m,k) ≠ C_qs⁽ⁿ⁾(m,k).