The minimal communication cost for simulating entangled qubits

We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, |TAB) = root p |00) + root 1 - p |11) (1/2 < p < 1). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by comally, when 2p(1-p) ( p ) 2p-1 log + 2(1 - p) < 1, approximately 0.835 < p < 1, we present a classical protocol that requires only a single bit of communication. The latter model even allows a perfect classical simulation with an average communication cost that approaches zero in the limit where the (p -> 1). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.