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According to Bell's theorem, certain entangled states cannot be simulatedclassically using local hidden variables (LHV). But if can we augment LHV byclassical communication, how many bits are needed to simulate them? There is astrong evidence that a single bit of communication is powerful enough tosimulate projective measurements on any two-qubit entangled state. In thisstudy, we present Bell-like scenarios where bipartite correlations resultingfrom projective measurements on higher dimensional states cannot be simulatedwith a single bit of communication. These include a three-input, a four-input,a seven-input, and a 63-input bipartite Bell-like inequality with 80089, 64,16, and 2 outputs, respectively. Two copies of emblematic Bell expressions,such as the Magic square pseudo-telepathy game, prove to be particularlypowerful, requiring a $16\times 16$ state to beat the one-bit classical bound,and look a promising candidate for implementation on an optical platform.

Beating one bit of communication with and without quantum pseudo-telepathy