Qutrit witness from the Grothendieck constant of order four
AbstractIn this paper, we prove that KG(3)<KG(4), where KG(d) denotes the Grothendieck constant of order d. To this end, we use a branch-and-bound algorithm commonly used in the solution of NP-hard problems. It has recently been proven that KG(3)≤1.4644. Here we prove that KG(4)≥1.4841, which has implications for device-independent witnessing dimensions greater than two. Furthermore, the algorithm with some modifications may find applications in various black-box quantum information tasks with large number of inputs and outputs.