Bures Distance and Transition Probability for alpha-CPD-Kernels

摘要

Given an automorphism alpha on a C-algebra, we obtain the Kolmogorov decomposition of alpha-completely positive definite kernels (or alpha-CPD-kernels for short) and investigate the Bures distance between alpha-CPD-kernels. We also define the transition probability for these kernels and find a characterization of the transition probability.