Towards nonadditive quantum information theory

A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon -Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis entropy. The nonadditive conditional entropy, when consider ed in the quantum context, is always positive for separable states but take s negative values for entangled states, indicating its utility for characte rizing entanglement. A criterion deduced from it for separability of the de nsity matrix is examined in detail by employing a bipartite spin-1/2 system . It is found that the strongest criterion for separability obtained by Per es using an algebraic method is recovered in the present information-theore tic approach in the limit q --> infinity. (C) 2001 Elsevier Science Ltd. Al l rights reserved.