An interesting protocol for classical teleportation of an unknown classicalstate 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, evenif Alice has absolutely no knowledge about P. Pursuing a similar line ofthought, we suggest here a limited form of nonlocality - "classicalnonlocality". Our nonlocality is the (somewhat limited) classical analogue ofthe Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocalitytells us how, for a given density matrix rho, Alice can generate anyrho-ensemble on the North Star. This is done using surprisingly few resources -one shared entangled state (prepared in advance), one generalized quantummeasurement, and no communication. Similarly, our classical nonlocalitypresents how, for a given probability distribution P, Alice can generate anyP-ensemble on the North Star, using only one correlated state (prepared inadvance), one (generalized) classical measurement, and no communication. It is important to clarify that while the classical teleportation and theclassical non-locality protocols are probably rather insignificant from aclassical information processing point of view, they significantly contributeto our understanding of what exactly is quantum in their well established andhighly famous quantum analogues.
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