The role of entanglement in dynamical evolution
Open accessAbstract
Entanglement or entanglement-generating interactions permit to achieve the maximum allowed speed in the dynamical evolution of a composite system, when the energy resources are distributed among subsystems. The cases of pre-existing entanglement and of entanglement-building interactions are separately addressed. The role of classical correlations is also discussed.
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Both the Mandelstam-Tamm and Margolus-Levitin bounds are valid, as shown by elementary proofs and by proofs for mixed and entangled states.
“That both bounds, ( 12) and (16), hold true, however, was illustrated by further elementary proofs by, e.g.Uffink [19], Brody [54], Andrecut and Ali [55], and Kosiński and Zych [56], and by more eleborated proofs for mixed and entangled states [57][58][59].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [57]
For unitary processes, entanglement is a resource that enhances the speed of evolution, so that the separation time improves from τ ∼ 1/√N (separable, slow state) to τ ∼ 1/N (entangled, fast state).
“It has already been seen in the literature [22-26] that, for unitary processes, entanglement is a resource that enhances the speed of evolution, so that the separation time improves from a τ ∼ 1 / √ N scaling (separable, slow state) to τ ∼ 1 /N (entangled, fast state).”
From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [23]
The speed limit for 1D QST could be overcome by increasing either network complexity or Hamiltonian complexity if not confined to nearest-neighbor interactions in one dimension.
“We lastly comment that such speed limit, if not confined with nearest-neighbor interactions in one dimension, could be overcome by increasing either the network complexity [9] or the Hamiltonian complexity [26].”
From Quantum speed limit for perfect state transfer in one dimension (2006) · cites this paper as [26]
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Cites
Ultimate physical limits to computation
Lloyd, S. (2000) · Nature · doi:10.1038/35023282 · Cited by 1,120 · see citing works
Self-citationThe maximum speed of dynamical evolution
Margolus, N., & Levitin, L. B. (1998) · Physica D: Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00054-2 · Cited by 887 · see citing works
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Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440 · see citing works
Self-citationQuantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c6 · Cited by 585 · see citing works
Enhancing the Charging Power of Quantum Batteries
Campaioli, F., Pollock, F. A., Binder, F. C., Céleri, L., Goold, J., Vinjanampathy, S., & Modi, K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.150601 · Cited by 531 · see citing works
Fundamental Limit on the Rate of Quantum Dynamics: The Unified Bound Is Tight
Levitin, L. B., & Toffoli, T. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.160502 · Cited by 302 · see citing works
Quantum speed limit for perfect state transfer in one dimension
Yung, M.-H. (2006) · Physical Review A · doi:10.1103/physreva.74.030303 · Cited by 128 · see citing works
Quantum coherence sets the quantum speed limit for mixed states
Mondal, D., Datta, C., & Sazim, S. (2016) · Physics Letters A · doi:10.1016/j.physleta.2015.12.015 · Cited by 113 · see citing works
Kind of entanglement that speeds up quantum evolution
Fröwis, F. (2012) · Physical Review A · doi:10.1103/physreva.85.052127 · Cited by 87 · see citing works
Quantum speed limit for mixed states using an experimentally realizable metric
Mondal, D., & Pati, A. K. (2016) · Physics Letters A · doi:10.1016/j.physleta.2016.02.018 · Cited by 78 · see citing works
Connection between entanglement and the speed of quantum evolution
Batle, J., Casas, M., Plastino, A., & Plastino, A. R. (2005) · Physical Review A · doi:10.1103/physreva.72.032337 · Cited by 75 · see citing works
The speed limit of quantum unitary evolution
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/8/028 · Cited by 62 · see citing works
Self-citationEntanglement and the lower bounds on the speed of quantum evolution
Borrás, A., Casas, M., Plastino, A. R., & Plastino, A. (2006) · Physical Review A · doi:10.1103/physreva.74.022326 · Cited by 63 · see citing works
Entanglement and the speed of evolution of multi-partite quantum systems
Zander, C., Plastino, A. R., Plastino, A., & Casas, M. (2007) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/40/11/020 · Cited by 52 · see citing works
- Authors
- Giovannetti, V, Lloyd, S., & Maccone, L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Europhysics Letters (EPL)
- Publisher
- IOP Publishing
- Published
- 2003-06
- Volume
- 62
- Issue
- 5
- Pages
- 615-621
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W2086310087
- Cited by
- 82
- References
- 2
- Citations by year
- 2026: 2 · 2025: 9 · 2024: 3 · 2023: 5 · 2022: 6 · 2021: 4 · 2020: 3 · 2019: 3 · 2018: 1 · 2017: 5 · 2016: 4 · 2015: 3 · 2014: 6 · 2013: 7 · 2012: 2
- FWCI
- 2.84
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Europhysics Letters (EPL) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum entanglement, dynamical evolution, composite systems, classical correlations
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