QUANTUM CORRELATIONS ON QUANTUM SPACES

For given quantum spaces, we study the quantum space of maps between them. We prove that, under certain conditions, the C*-algebra of this quantum space enjoys the lifting property and is residually finite dimensional. We construct a universal operator system inside this C*-algebra, and unravel its several interesting properties, including the hyperrigidity of its embedding. Then we apply this construction to study classes of quantum correlations. Finally, we discuss the notion of synchronicity within this framework. This talk is based on joint work with P. Kasprzak and P. M. Sołtan.