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Cited by 417Quantum Mechanics and Non-Hermitian PhysicsQuantum Mechanics and ApplicationsQuantum chaos and dynamical systems

The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.

Faster than Hermitian Quantum Mechanics

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Bender, Carl M., Brody, Dorje C., Jones, Hugh F., Meister, Bernhard K.·2007·Physical Review Letters
DOI 10.1103/physrevlett.98.040403
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Abstract

Given an initial quantum state $|{\ensuremath{\psi}}_{I}⟩$ and a final quantum state $|{\ensuremath{\psi}}_{F}⟩$, there exist Hamiltonians $H$ under which $|{\ensuremath{\psi}}_{I}⟩$ evolves into $|{\ensuremath{\psi}}_{F}⟩$. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of $H$ is held fixed, which $H$ achieves this transformation in the least time $\ensuremath{\tau}$? For Hermitian Hamiltonians $\ensuremath{\tau}$ has a nonzero lower bound. However, among non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians satisfying the same energy constraint, $\ensuremath{\tau}$ can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from $|{\ensuremath{\psi}}_{I}⟩$ to $|{\ensuremath{\psi}}_{F}⟩$ can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.

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Metadata

Authors
Bender, C. M., Brody, D. C., Jones, H. F., & Meister, B. K.
Affiliations
  • Washington University in St. Louis (US)
  • Imperial College London (GB)
  • Renmin University of China (CN)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2007-01-24
Volume
98
Issue
4
Pages
040403-040403
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.98.040403
OpenAlex
W2010599738
Cited by
417
References
20
Citations by year
2026: 23 · 2025: 25 · 2024: 26 · 2023: 23 · 2022: 29 · 2021: 26 · 2020: 28 · 2019: 28 · 2018: 28 · 2017: 24 · 2016: 18 · 2015: 18 · 2014: 16 · 2013: 16 · 2012: 24
FWCI
10.16
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (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 › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
Keywords
quantum brachistochrone, non-Hermitian Hamiltonian, PT-symmetric Hamiltonians, time-energy uncertainty relation, quantum state evolution, energy constraints, Hamiltonian spectrum, quantum computing

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