  Based on the form invariance of the structures given by Khinchin's axiomatic
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 nonadditive
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 matrices
for validity of local realism is examined in detail by employing a bipartite
spin-1/2 system. It is found that the strongest criterion is obtained in the
limit q going to infinity.
