Nonadditive conditional entropy and its significance for local realism

Based on the form invariance of the structures given by Khinchin's axiomati c foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of nonadditive (nonextensive) composite systems. The proposed non additive conditional entropy is classically nonnegative but can be negative in the quantum context, indicating its utility for characterizing quantum entanglement. A criterion deduced from it for separability of density matri ces for validity of local realism is examined in detail by employing a bipa rtite spin-1/2 system. It is found that the strongest criterion is obtained in the limit g --> infinity. (C) 2001 Elsevier Science B.V. Air rights res erved.