摘要 : D. Bures defined a metric beta on states of a C*-algebra and this concept has been generalized to unital completely positive maps phi : A -> B, where B is either an injective C*-algebra or a von Neumann algebra. We introduce a new... 展开 D. Bures defined a metric beta on states of a C*-algebra and this concept has been generalized to unital completely positive maps phi : A -> B, where B is either an injective C*-algebra or a von Neumann algebra. We introduce a new distance gamma for the same classes of unital completely positive maps. We use in our definition the distance between representations on the same Hilbert C*-module in contrast to the Bures metric which uses one representation and distinct vectors. This metric can be expressed in terms of a class of completely positive maps on free products of C*-algebras and in this setting gamma looks like Wasserstein metric on probability measures. Surprisingly, when the range algebra B is injective, gamma and beta are related by the following explicit formula: beta(2) = 2 - root 4 - gamma(2). A deep result of Choi and Li on constrained dilation is the main tool in proving this formula. 收起