Towards a quantum sampling theory: the case of finite groups
Mathematical Physics
2019-05-16 v1 math.MP
Abstract
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group . Two main ideas from the classical theory having natural counterparts in the quantum setting: frames and invariant subspaces, provide the mathematical background for the theory. The main ingredients of classical sampling theorems are discussed and their quantum counterparts are thoroughly analyzed in this simple situation. A few examples illustrating the obtained results are discussed.
Keywords
Cite
@article{arxiv.1510.08134,
title = {Towards a quantum sampling theory: the case of finite groups},
author = {Antonio G. García and Miguel A. Hernández-Medina and A. Ibort},
journal= {arXiv preprint arXiv:1510.08134},
year = {2019}
}