Fidelity and entanglement fidelity for infinite-dimensional quantum systems
Li Wang, Jinchuan Hou, Xiaofei Qi · Journal of Physics A Mathematical and Theoretical · 2014
Instead of unitary freedom for finite-dimensional cases, bi-contractive freedom in the operator-sum representation for quantum channels of infinite-dimensional systems is established. Specifically, if the channel sends every pure state to a finite rank state, then the isometric freedom feature holds. Then, a method of computing entanglement fidelity and a relation between quantum fidelity and entanglement fidelity for infinite-dimensional systems are obtained. In addition, upper and lower bounds of the quantum fidelity, and their connection to the trace distance, are also provided.