  Game theory is a well established branch of mathematics whose formalism has a
vast range of applications from the social sciences, biology, to economics.
Motivated by quantum information science, there has been a leap in the
formulation of novel game strategies that lead to new (quantum Nash)
equilibrium points whereby players in some classical games are always
outperformed if sharing and processing joint information ruled by the laws of
quantum physics is allowed. We show that, for a bipartite non zero-sum game,
input local quantum correlations, and separable states in particular, suffice
to achieve an advantage over any strategy that uses classical resources, thus
dispensing with quantum nonlocality, entanglement, or even discord between the
players' input states. This highlights the remarkable key role played by pure
quantum coherence at powering some protocols. Finally, we propose an experiment
that uses separable states and basic photon interferometry to demonstrate the
locally-correlated quantum advantage.
