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
Open accessAbstract
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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“Bender et al [249] then argued that PT -symmetric Hamiltonians provide means to accelerate quantum mechanics.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [249]
In the citing paper
“However, Bender et al [249] also note that such |ψ 0 and |ψ T are no longer orthogonal, since under PT -symmetric Hamiltonians the inner product, and hence the geometry of Hilbert space has to be modified (137).”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [249]
Citations
Cites
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Self-citationQuantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,160
Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity
Morris, M. S., & Thorne, K. S. (1988) · American Journal of Physics · doi:10.1119/1.15620 · Cited by 3,009
Complex Extension of Quantum Mechanics
Bender, C. M., Brody, D. C., & Jones, H. F. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.270401 · Cited by 1,803
Self-citationMostafazadeh, A. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1418246 · Cited by 1,645
Wormholes, Time Machines, and the Weak Energy Condition
Morris, M. S., Thorne, K. S., & Yurtsever, U. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1446 · Cited by 1,609
𝓟𝓣-symmetric quantum mechanics
Bender, C. M., Boettcher, S., & Meisinger, P. N. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532860 · Cited by 1,379
Self-citationAnandan, J., & Aharonov, Y. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.1697 · Cited by 794
Mostafazadeh, A. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1489072 · Cited by 788
Dorey, P., Dunning, C., & Tateo, R. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/28/305 · Cited by 544
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Observation of parity–time symmetry in optics
Rüter, C. E., Makris, K. G., El‐Ganainy, R., Christodoulides, D. N., Segev, M., & Kip, D. (2010) · Nature Physics · doi:10.1038/nphys1515 · Cited by 3,564
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
Self-citationObservation of P T -Symmetry Breaking in Complex Optical Potentials
Guo, A., Salamo, G. J., Duchesne, D., Morandotti, R., Volatier, M., Aimez, V., Siviloglou, G. A., & Christodoulides, D. N. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.093902 · Cited by 2,723
Beam Dynamics in P T Symmetric Optical Lattices
Makris, K. G., El‐Ganainy, R., Christodoulides, D. N., & Musslimani, Z. H. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.103904 · Cited by 2,046
Unidirectional Invisibility Induced by P T -Symmetric Periodic Structures
Lin, Z., Ramezani, H., Eichelkraut, T., Kottos, T., Cao, H. W., & Christodoulides, D. N. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.213901 · Cited by 1,905
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)
- 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
- 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
- green
- arxiv.org
- 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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