Information Content of Systems as a Physical Principle
  To explain conceptual gap between classical/quantum and other, hypothetical descriptions of world, several principles has been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce an information content principle (ICP) which represents the new - constrained uncertainty principle. The principle, by taking into account the encoding/decoding properties of single physical system, is capable of separation both classicality and quanta from a number of potential physical theories including hidden variable theories. The ICP, which is satisfied by both classical and quantum theory, states that the amount of non-redundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that ICP allows to discriminate theories which do not allow for correlations stronger than Tsirelson's bound. We show also how to apply the principle to composite systems, ruling out some theories despite their elementary constituents behave quantumly. 
L. Czekaj, M. Horodecki, P. Horodecki, R. Horodecki
quant-ph cs.IT math.IT