Time-dependent Hamiltonians with 100% evolution speed efficiency
Abstract
The evolution speed in projective Hilbert space is considered for Hermitian Hamiltonians and for non-Hermitian (NH) ones. Based on the Hilbert-Schmidt norm and the spectral norm of a Hamiltonian, resource-related upper bounds on the evolution speed are constructed. These bounds are valid also for NH Hamiltonians and they are illustrated for an optical NH Hamiltonian and for a non-Hermitian symmetric matrix Hamiltonian. Furthermore, the concept of quantum speed efficiency is introduced as measure of the system resources directly spent on the motion in the projective Hilbert space. A recipe for the construction of time-dependent Hamiltonians which ensure 100% speed efficiency is given. Generally these efficient Hamiltonians are NH but there is a Hermitian efficient Hamiltonian as well. Finally, the extremal case of a non-Hermitian non-diagonalizable Hamiltonian with vanishing energy difference is shown to produce a 100% efficient evolution with minimal resources consumption.
Keywords
Cite
@article{arxiv.1207.5373,
title = {Time-dependent Hamiltonians with 100% evolution speed efficiency},
author = {Raam Uzdin and Uwe Guenther and Saar Rahav and Nimrod Moiseyev},
journal= {arXiv preprint arXiv:1207.5373},
year = {2012}
}