Nonadditive information measure and quantum entanglement in a class of mixed states of an Nⁿ system

Generalizing Khinchin’s classical axiomatic foundation, a basis is developed for nonadditive information theory with the Tsallis entropy indexed by q. The classical nonadditive conditional entropy is introduced and then translated into quantum theory. To examine if this theory has points superior to the ordinary additive information theory with the von Neumann entropy corresponding to the limit q→1, separability of a one-parameter family of the Werner-Popescu states of the Nⁿ system (i.e., the n-partite N-level system) is discussed. The nonadditive information theory with q>1 is shown to yield a limitation on separability that is stronger than the one derived from the additive theory. How the strongest limitation can be obtained in the limit q→∞ is also shown.