Special functions in quantum phase estimation
Quantum Physics
2023-02-15 v1 Mathematical Physics
math.MP
Abstract
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which approximately gives the maximum probability that the difference between the true parameter and the estimate is smaller than a certain threshold. The other is Mathieu function, which exactly gives the optimum estimation under the energy constraint. It also characterizes the uncertainty relation for the position and the momentum for periodic functions.
Cite
@article{arxiv.2302.06899,
title = {Special functions in quantum phase estimation},
author = {Masahito Hayashi},
journal= {arXiv preprint arXiv:2302.06899},
year = {2023}
}