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Through the generalization of Khinchin's classical axiomatic foundation, abasis is developed for nonadditive information theory. The classicalnonadditive conditional entropy indexed by the positive parameter q isintroduced and then translated into quantum information. This quantity isnonnegative for classically correlated states but can take negative values forentangled mixed states. This property is used to study quantum entanglement inthe parametrized Werner-Popescu-like state of an N^n-system, that is, ann-partite N-level system. It is shown how the strongest limitation on validityof local realism (i.e., separability of the state) can be obtained in a novelmanner

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

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Nonadditive information measure and quantum entanglement in a class of mixed states of anNnsystem