Some properties of quantum fidelity in infinite-dimensional quantum systems

摘要

In this paper, we review the infinite-dimensional version of Uhlmann's theorem of quantum fidelity. Based on this important theorem, we derive some useful properties of quantum fidelity for in finite-dimensional quantum systems. Next, we study the fidelity in the in finite-dimensional discrete-time quantum filters associated Markov chain, and prove that it is a sub-martingale.