Comment on “Geometric derivation of the quantum speed limit”
Open accessAbstract
Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus-Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed in terms of the standard deviation of the generator $K$ and its expectation value above the ground state. The bounds lead to the Mandelstam-Tamm inequality and a quantum speed limit which is only slightly weaker than the Margolus-Levitin inequality.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Generalizations of the Mandelstam-Tamm and Margolus-Levitin findings to nonorthogonal states and driven systems have been provided in prior work.
“Generalizations of the MT and ML findings to nonorthogonal states and to driven systems have been provided in Refs.[14][15][16][17][18][19].”
From Quantum Speed Limit for Non-Markovian Dynamics (2013) · cites this paper as [16]
The statistical distance is the natural choice to define the maximal quantum speed.
“Since ℓ constitutes the shortest path connecting quantum states, the statistical distance (67) serves as the natural choice to define the maximal quantum speed [60,67,75,76,117].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [76]
Equation (30) is the Margolus-Levitin bound for quantum systems evolving under time-independent Hamiltonians, valid for arbitrary angles between initial and final states; it corrects previously published versions.
“Equation (30) is the Margolus-Levitin bound for quantum systems evolving under time-independent Hamiltonians, valid for arbitrary angles between initial and final states; it corrects previously published versions [18, 43].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [43]
The geometric derivation of the Margolus-Levitin bound put forward in Ref. [18] does not hold true in general.
“It has lately been recognized that the geometric derivation of the Margolus-Levitin bound put forward in Ref. [18] does not hold true in general [43].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [43]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
The 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
Geometric derivation of the quantum speed limit
Jones, P. J., & Kok, P. (2010) · Physical Review A · doi:10.1103/physreva.82.022107 · Cited by 172 · see citing works
Flagged first, then by citations
Research works printed but not linked: 8
- P. J. Jones and P. Kok, Phys. Rev. A 82, 022107 (2010).
- L. Mandelstam and I. Tamm, J. Phys. (USSR) 9, 249 (1945).
- N. Margolus and L. B. Levitin, Phys. D 120, 188 (1998).
- W. K. Wootters, Phys. Rev. D 23, 357 (1981).
- J. Anandan and Y. Aharonov, Phys. Rev. Lett. 65, 1697 (1990).
- K. Bhattacharyya, J. Phys. A: Math. Gen. 16, 2993 (1983).
- S. L. Braunstein, C. M. Caves, and G. J. Milburn, Ann. Phys. 247, 135 (1996).
- S. Deffner and E. Lutz, arXiv:1104.5104v2. · arXiv
Cited by
Sorted by citations
Quantum 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
Quantum Speed Limit for Non-Markovian Dynamics
Deffner, S., & Lutz, E. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.010402 · Cited by 511 · see citing works
Quantum Speed Limits in Open System Dynamics
del Campo, A., Egusquiza, I. L., Plenio, M. B., & Huelga, S. F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.050403 · Cited by 493 · see citing works
Energy–time uncertainty relation for driven quantum systems
Deffner, S., & Lutz, E. (2013) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/46/33/335302 · Cited by 199 · see citing works
Quantum speedup in a memory environment
Xu, Z.-Y., Luo, S., Yang, W. L., Liu, C., & Zhu, S. (2014) · Physical Review A · doi:10.1103/physreva.89.012307 · Cited by 156 · see citing works
Classical-driving-assisted quantum speed-up
Zhang, Y.-J., Han, W., Xia, Y.-J., Cao, J.-P., & Fan, H. (2015) · Physical Review A · doi:10.1103/physreva.91.032112 · Cited by 95 · see citing works
Quantum-speed-limit time for multiqubit open systems
Liu, C., Xu, Z.-Y., & Zhu, S. (2015) · Physical Review A · doi:10.1103/physreva.91.022102 · Cited by 83 · 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
Quantum speed limit and optimal evolution time in a two-level system
Poggi, P. M., Lombardo, F. C., & Wisniacki, D. A. (2013) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/104/40005 · Cited by 70 · see citing works
APPLICATIONS OF FINSLER GEOMETRY TO SPEED LIMITS TO QUANTUM INFORMATION PROCESSING
RUSSELL, B., & STEPNEY, S. (2014) · International Journal of Foundations of Computer Science · doi:10.1142/s0129054114400073 · Cited by 15 · see citing works
- Authors
- Zwierz, M.
- Affiliations
- Griffith University (AU)
- Corresponding author
- Zwierz, Marcin
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-07-09
- Volume
- 86
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2001492459
- Cited by
- 72
- References
- 2
- Citations by year
- 2026: 1 · 2025: 9 · 2024: 3 · 2023: 4 · 2022: 2 · 2021: 6 · 2020: 8 · 2019: 3 · 2018: 5 · 2017: 5 · 2016: 5 · 2015: 7 · 2014: 7 · 2013: 7
- FWCI
- 6.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- Griffith Research Online (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- quantum speed limit, statistical distance, geometric derivation, ground state
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
