On classical teleportation and classical non-locality

An interesting protocol for classical teleportation of an unknown classical state was recently suggested by Cohen, and by Gour and Meyer. In that protocol, Bob can sample from a probability distribution P that is given to Alice, even if Alice has absolutely no knowledge about P. Pursuing a similar line of thought, we suggest here a limited form of non-locality - "classical non-locality." Our non-locality is the (somewhat limited) classical analogue of the Hughston-Jozsa-Wootters (HJW) quantum non-locality. The HJW non-locality (also known as "quantum remote steering") tells us how, for a given density matrix p, Alice can generate any p-ensemble on the North Stax. This is done using surprisingly few resources - one shared entangled state (prepared in advance), one generalized quantum measurement, and no communication. Similarly, our classical nonlocality (which we call "classical remote steering") presents how, for a given probability distribution P, Alice can generate any P-ensemble on the North Star, using only one correlated state (prepared in advance), one (generalized) classical measurement, and no communication. It is important to clarify that while the classical teleportation and the classical non-locality protocols are probably rather insignificant from a classical information processing point of view, they significantly contribute to our understanding of what exactly is quantum in their well established and highly famous quantum analogues.