Time-dependent Hamiltonians with 100% evolution speed efficiency
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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 -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.
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Because the Bures angle can be near 1 for one same-spectrum pair while near 0 for another, and the denominator may differ, the Bures bound cannot be tight for mixed states.
“Even though the denominator of Eq. ( 1) may in principle also differ between these two scenarios due to its state dependence [47], that bound cannot be tight for the case of mixed states.”
From Tightening Quantum Speed Limits for Almost All States (2018) · cites this paper as [47]
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Self-citation
- Authors
- Uzdin, R., Günther, U., Rahav, S., & Moiseyev, N.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Helmholtz-Zentrum Dresden-Rossendorf (DE)
- Corresponding author
- Uzdin, Raam
- Venue
- Journal of Physics A: Mathematical and Theoretical
- Publisher
- IOP Publishing
- Published
- 2012-09-25
- Volume
- 45
- Issue
- 41
- Pages
- 415304
- ISSN
- 1751-8113 (ISSN-L)
- 1751-8121
- OpenAlex
- W2107734295
- Cited by
- 54
- References
- 69
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 8 · 2022: 5 · 2020: 5 · 2019: 3 · 2018: 2 · 2017: 5 · 2016: 2 · 2015: 5 · 2014: 2 · 2013: 5 · 2012: 1
- FWCI
- 2.15
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and Theoretical (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- time-dependent Hamiltonian, quantum speed limit, projective Hilbert space, non-Hermitian Hamiltonian, Hermitian Hamiltonian, Frobenius norm, spectral norm, resource consumption, PT-symmetric Hamiltonians
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