Qutrit witness from the Grothendieck constant of order four

Diviánszky, Péter and Bene, Erika and Vértesi, Tamás (2017) Qutrit witness from the Grothendieck constant of order four. PHYSICAL REVIEW A, 96 (1). ISSN 2469-9926

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Abstract

In 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. © 2017 American Physical Society.

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