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 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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2012
- DOI:
- 10.1088/1751-8113/45/41/415304
- arXiv:
- arXiv:1207.5373
- Bibcode:
- 2012JPhA...45O5304U
- Keywords:
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- Quantum Physics
- E-Print:
- J. Phys. A: Math. Theor. 45, (2012), 415304