The speed limit of quantum unitary evolution
Open accessAbstract
How fast can a quantum system evolve? In this paper we study the relation between entanglement and the time it takes for a composite system to perform a given evolution. In particular, we analyse how the order of the interactions shapes the dynamics.
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Giovannetti, Lloyd, and Maccone numerically established that for time-independent Hamiltonians the quantum speed limit time is τ_QSL = max(ΔH L, (2/π)⟨H⟩ L^2).
“For time-independent Hamiltonians Giovannetti, Lloyd, and Maccone [71][72][73] established numerically that the quantum speed limit time has to be given by τ QSL = max ∆H L (ρ 0 , ρ τ ) , 2 π H L 2 (ρ 0 , ρ τ ) .(34)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [73]
The above expression generalizes in a unified manner previous results derived in Refs. [7-22].
“The above expression generalizes in an unified manner previous results derived in Refs. [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [16]
For many physical systems, both k and m are limited: 2 or 3-body interactions are the norm for fundamental processes, and higher interaction orders are generally hard to engineer.
“For many physical systems, both k and m are limited: 2 or 3-body interactions are the norm for fundamental processes, and higher interaction orders are generally hard to engineer here [37-39].”
From Enhancing the Charging Power of Quantum Batteries (2017) · cites this paper as [37]
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 [24]
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“[46] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone, “The speed limit of quantum unitary evolution,” Journal of Optics B: Quantum and Semiclassical Optics 6, S807–S810 (2004).”
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“[11–13].”
Geometric Quantum Speed Limits and Time-Cost Trade-Off in Time-Dependent Quantum ControlPreprint
Tao, H. G., & Jin, Z. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7519472
- Authors
- Giovannetti, V., Lloyd, S., & Maccone, L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Journal of Optics B: Quantum and Semiclassical Optics
- Publisher
- IOP Publishing
- Published
- 2004-07-28
- Volume
- 6
- Issue
- 8
- Pages
- S807-S810
- ISSN
- 1464-4266 (ISSN-L)
- 1741-3575
- OpenAlex
- W1971702154
- Cited by
- 62
- References
- 13
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 6 · 2023: 9 · 2022: 5 · 2021: 4 · 2020: 3 · 2019: 1 · 2018: 5 · 2017: 6 · 2016: 4 · 2015: 4 · 2014: 2 · 2013: 2 · 2012: 1
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Optics B Quantum and Semiclassical Optics (publishedVersion)
- Scuola Normale Superiore di Pisa (submittedVersion)
- Funders
- National Science Foundation
- Agricultural Research Development Agency
- Multidisciplinary University Research Initiative
- Army Research Office
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum speed limit, entanglement, composite quantum systems, interaction order, quantum dynamics, time evolution of quantum systems
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