完全有界p-模的乘法性蕴涵了一个新的可加性结果
Multiplicativity of completely bounded p-norms implies a new additivity result
摘要：
本文证明了当S（gamma_{12}）- S（gamma_1）的下确界被限制为gamma_{12} =（I \ot Phi）（|psi >< psi|).我们证明了这是由矩阵上Schatten p-范数定义的L_p空间的φ的完全有界范数的乘法性所导致的，并基于熵不等式给出了一个独立的证明.讨论并证明了几个相关的乘法性结果。特别地，我们证明了CP映射的通常的L_1 -> L_p范数和相应的完全有界范数对于半正定矩阵都是成立的。物理解释被认为是，并提出了一个新的证明强次可加性。
英文摘要：
We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p 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 L_1 -> L_p 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.
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