This question was first considered by Boris Tsirelson in 1993, where he asserted without proof that formula_40. Upon being asked for a proof by Antonio Acín in 2006, he realized that the one he had in mind didn't work, and issued the question as an open problem. Together with Miguel Navascués and Stefano Pironio, Antonio Acín had developed an hierarchy of semidefinite programs, the NPA hierarchy, that converged to the commuting Tsirelson bound formula_42 from above, and wanted to know whether it also converged to the tensor product Tsirelson bound formula_43, the most physically relevant one.