Reduction of unitary operators, quantum graphs and quantum channels
Quantum Physics
2025-01-10 v2 Mathematical Physics
math.MP
Abstract
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices of new quantum graphs from assembling of simpler graphs. The reduction of quantum channels is also defined. The implementation of the quantum gates corresponding to the reduced unitary operator is investigated, although no explicit construction is presented. The situation is different for the reduction of quantum channels for which explicit implementations are given.
Cite
@article{arxiv.2407.19536,
title = {Reduction of unitary operators, quantum graphs and quantum channels},
author = {L. L. Salcedo},
journal= {arXiv preprint arXiv:2407.19536},
year = {2025}
}
Comments
16 pages, 8 figures. Title changed. The original nomenclature "contraction" has been changed to "reduction" throughout the manuscript