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arXiv · 1207.5373

Time-dependent Hamiltonians with 100% evolution speed efficiency

Raam Uzdin·Uwe Guenther·Saar Rahav·Nimrod Moiseyev
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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 $\mathcal{PT}-$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.

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Raam Uzdin, Uwe Guenther, Saar Rahav, Nimrod Moiseyev. 2012-07-23. Time-dependent Hamiltonians with 100% evolution speed efficiency. https://doi.org/10.1088/1751-8113%2F45%2F41%2F415304

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