Time-dependent Hamiltonians with 100% evolution speed efficiency

Raam Uzdin*, Uwe Günther, Saar Rahav, Nimrod Moiseyev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 NH 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 NH non-diagonalizable Hamiltonian with vanishing energy difference is shown to produce a 100% efficient evolution with minimal resources consumption.

Original languageAmerican English
Article number415304
JournalJournal of Physics A: Mathematical and Theoretical
Issue number41
StatePublished - 19 Oct 2012
Externally publishedYes


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