Simulating maximal quantum entanglement without communication

It is known that all causal correlations between two parties which output each 1 bit, a and b, when receiving each 1 bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and nonlocal correlations of the form a+b=xy mod 2. We show that a single instance of the latter elementary nonlocal correlation suffices to simulate exactly all possible projective measurements that can be performed on a maximally entangled state of two qubits, with no communication needed at all. This elementary nonlocal correlation thus defines some unit of nonlocality, which we call a nl bit.