ua nt - p h / 05 06 19 6 v 1 2 3 Ju n 20 05 Multiplicativity of completely bounded p - norms implies a new additivity result Igor
نویسندگان
چکیده
We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I⊗Φ) ( |ψ〉〈ψ| ) . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L1 → Lp norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.
منابع مشابه
ua nt - p h / 05 06 19 6 v 2 2 3 Ja n 20 06 Multiplicativity of completely bounded p - norms implies a new additivity result
We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represent by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I ⊗Φ) ( |ψ〉〈ψ| ) We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatten ...
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