A recent article introduced a hierarchy of quantities called k-fidelities that approximate the quantum process fidelity with increasing accuracy. The lowest approximation in this hiearchy is the 0-fidelity. The authors gave a protocol for estimating the 0-fidelity and showed numerical evidence that it approximates the process fidelity. In this note, we prove lower and upper bounds on the process fidelity as linear functions of the 0-fidelity. By solving a semidefinite program, we provide evidence that the lower bound is tight.
Cite
@article{arxiv.2109.09629,
title = {A short note on the 0-fidelity},
author = {Karl Mayer},
journal= {arXiv preprint arXiv:2109.09629},
year = {2021}
}