Suppose Alice and Bob share a maximally entangled state of any finite dimension and each perform two-outcome measurements on the respective part of the state. It is known, due to the recent result of Regev and Toner, that if a classical model is augmented with two bits of communication, then all the quantum correlations arising from these measurements can be reproduced. Here, we show that two bits of communication are in fact necessary for the perfect simulation. In particular, we prove that a pair of maximally entangled four-dimensional quantum systems cannot be simulated by a classical model augmented by only one bit of communication.

• Received 8 April 2009

DOI:https://doi.org/10.1103/PhysRevA.80.062316