we will discuss quantum no-signaling correlations introduced by duan and winter with focus on its different subclasses (quantum commuting, quantum and local). they will appear as strategies of quantum-to-quantum non-local games. we will then discuss concurrent quantum non-local games, as quantum versions of synchronous/bisynchronous non-local games focusing on quantum graph homomorphism/isomorphism games, and provide tracial characterisations of their perfect strategies belonging to various correlation classes; e.g. the perfect strategies for quantum graph isomorphism game are given by tracial states on the universal c∗-algebra of the projective free unitary quantum group. this is a joint work with michael brannan, sam harris and ivan todorov.