On the relation between Bell inequalities and nonlocal games

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We investigate the relation between Bell inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bell inequality, the converse is not true. As an illustration of the method we present a number of nonlocal games that admit better odds when played using quantum resources
v3 changes: Updates to reflect PLA version. 1 examples changed. Physics Letters A (accepted for publication)

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