Towards Nonadditive Quantum Information Theory

Details Towards Nonadditive Quantum Information Theory Towards Nonadditive Quantum Information Theory

2000-03-30

arxiv.org/abs/quant-ph/0003145v1

Physics

Quantum Physics

12 pages. Invited talk at International Workshop on Classical and Quantum Complexity and Nonextensive Thermodynamics (3-6 Apri

Scientific paper

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 considered in the quantum context, is always positive for separable states but takes negative values for entangled states, indicating its utility for characterizing entanglement. A criterion deduced from it for separability of the density matrix is examined in detail by using a bipartite spin-half system. It is found that the strongest criterion for separability obtained by Peres using an algebraic method is recovered in the present information-theoretic approach.

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