Almost synchronous quantum correlations

The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated questions foundations mechanics has more recently been tied to cryptography, complexity theory, operator space group more. Synchronous introduced [Paulsen et. al, JFA 2016] are a subclass correlations that proven particularly useful arises naturally applications. We show any is almost synchronous, natural $\ell_1$ sense, from state measurement operators well-approximated convex combination projective measurements on maximally entangled state. This extends result which applies exactly synchronous correlations. Crucially, quality approximation independent dimension Hilbert spaces or size correlation. Our allows one reduce analysis many classes nonlocal games, including rigidity properties, case strategies using states generally easier manipulate.