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Geometric derivation of the quantum speed limit
Open accessAbstract
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
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TL;DR
The paper gives alternative geometric derivations of the Mandelstam-Tamm and Margolus-Levitin quantum speed-limit inequalities from the statistical distance between quantum states. It shows these bounds hold for unitary evolution of pure and mixed states, and constructs a completely positive trace-preserving map counterexample that violates both, implying no general quantum speed limit for non-unitary evolution.
Key findings
- Both inequalities are derived geometrically: Mandelstam-Tamm follows from the Fisher-information bound, while Margolus-Levitin follows from explicit differentiation of the Wootters distance and the Cauchy-Schwarz inequality.
- The inequalities are shown to hold for unitary evolution of pure and mixed states; for mixed states, Margolus-Levitin is extended via purification, with the bound interpreted using the system’s average energy by choosing purifications made only of degenerate ground eigenstates.
- A counterexample using a central qubit plus \(N\) satellite qubits, GHZ entanglement, phase shifts, and simultaneous CZ/Hadamard gates produces orthogonal initial and final states in time \(t < \pi\hbar/E_0\) when \(N\phi=\pi\), with \(E_\phi > E_0\) and \(g\) chosen appropriately; this violates both bounds and shows \(t\) can be made arbitrarily small by making \(E_\phi\) and \(g\) arbitrarily large.
- The paper notes that mixed states can never attain either equality, and that states attaining the inequalities have the form of superpositions of energy eigenstates.
Methods
- Theoretical derivation with no experimental data or sample; the work is a mathematical/geometric analysis of quantum speed limits.
- Uses statistical distance for classical probability distributions and density matrices, Fisher information, Wootters distance, and Uhlmann purification to derive bounds on dynamical speed.
- The non-unitary counterexample is analyzed with the stabilizer formalism for \(N+1\) qubits, including CZ, Hadamard, and phase-shift gates, and gate-time periodicity arguments.
Limitations
- The paper states open questions: what general system-environment requirements allow violation of the speed limit; whether the strong interaction can be achieved noiselessly; whether noise may impose a practical speed limit; and whether general bounds can be based on environment properties rather than detailed dynamics.
- The paper states the counterexample “may be very difficult to implement in practice” and that \(t\) can be made arbitrarily small by making \(E_\phi\) and \(g\) arbitrarily large.
- Evident from the text: the counterexample is an idealized mathematical construction assuming simultaneous ideal gates and no noise; the mixed-state equality result is cited from prior work, and the derivation of the inequalities assumes unitary evolution.
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15 No basis given · 13 Own interpretation · 8 Not checked yet · 2 Own result
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In the paper
“It is straightforward to check that the state state corresponding to these stabilizer generators is the GHZ state ( | 0 , . . . , 0 〉 + | 1 , . . . , 1 〉 ) / √ 2 on the N + 1 qubits.”
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“we arrive at the conclusion that all N CZ gates can be applied simultaneously.”
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“In the case where K is the Hamiltonian and q the time, the inequality becomes the Margolus-Levitin inequality”
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“This is orthogonal to the initial state of the central qubit when N f = p .”
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“A similar argument holds for the application of the phase shifts on the satellite qubits, leading to t ( N ) f = t f .”
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In the paper
“The Mandelstam-Tamm and Margolus-Levitin inequalities do not hold for the most general quantum evolutions, described by completely positive, trace preserving maps (CP maps).”
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“we need to show that we can choose parameters such that t < p ¯ h / E 0.”
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- Rests on an assumption: The Hadamard gate evolves a state halfway to an orthogonal state.
In the paper
“In the case of pure quantum states this distance simplifies considerably, and we obtain the Wootters distance [8].”
What the sources say
- Not checked yetcites [8] W. K. Wootters, Phys. Rev. D 23 , 357 (1981). source
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In the paper
“a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“In the case where q is the time parameter generated by the Hamiltonian H , the inequality reduces to the famous Mandelstam-Tamm inequality”
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- It may state two separate claims as one. 5
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- Probably not a substantial claim. 4
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In the paper
“Since [ Hj , Hk ] = 0 for all j and k , the interaction Hamiltonian for the N CZ gates is H = j Hj .”
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In the paper
“In other words, the satellite qubits are back to their initial state, and the central qubit is in the state”
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In the paper
“In other words, the statistical distance in the space of probability distributions is the Euclidean distance in the space of (real) probability amplitudes.”
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In the paper
“The periodicity of Sj ( t ) then implies the periodicity of S 0 ( t ) , and moreover, they must have the same period.”
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In the paper
“If | y 〉 and | f 〉 are two arbitrary pure quantum states in Hilbert space, then the statistical distance is given by the angle between the two states:”
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In the paper
“Notice how the Wootters distance is related to the fidelity |〈 y | f 〉| 2 , which is the probability of mistaking | y 〉 for | f 〉 in a single-shot measurement.”
What the sources say
- Not checked yetcites [8] W. K. Wootters, Phys. Rev. D 23 , 357 (1981). source
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In the paper
“The counterexample presented here suggests that the interaction between the system and its environment must be strong, and that the environment must be more energetic than the system ( Eq > E 0).”
hedgeddirectSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“which can be interpreted as the probability of mistaking r for s in a single-shot measurement.”
What the sources say
- Not checked yetcites [17] R. Jozsa, J. Mod. Opt. 41 , 2315 (1994). source
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The paper relies on this without support.
To date there has been only one derivation of the Margolus-Levitin inequality.
“However, to date there has been only one derivation of the Margolus-Levitin inequality.”
The paper relies on this without support.
The purification is merely a mathematical construction, so unrestricted amounts of energy may be added to the system during the process and any extra energy added is physically meaningless.
“At first glance this seems problematic since the purification is merely a mathematical construction and therefore unrestricted amounts of energy may be added to the system during the process.”
The paper relies on this without support.
The Hadamard gate evolves a state halfway to an orthogonal state.
“The Hadamard gate evolves a state halfway to an orthogonal state, and the speed limit for this gate can therefore be taken as half the time given in Eq. (45), with E 0 → Eq :”
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?
In the citing paper
“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 [15]
In the citing paper
“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 [75]
In the citing paper
“The fundamental difference, however, becomes obvious for parameterised, driven, and time-dependent L(ρ t ) [75].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [75]
In the citing paper
“The above derivation can be extended to arbitrary mixed states by interpreting pure states as purifications of mixed states in an enlarged Hilbert space [35]. Specifically, by choosing the purification that maximizes the fidelity between two density operators, the Margolus-Levitin inequality also applies to the purifications [18].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [18]
In the citing paper
“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 [18]
In the citing paper
“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 [18]
In the citing paper
“Note that d t L is positive at short times, since L is initially zero (0 ≤ L ≤ π/ 2). However, the derivative may change sign later on, and special care should be taken when deriving inequalities (this fact seems not have been noticed by Jones and Kok [18]).”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [18]
In the citing paper
“The corresponding inequality is an extension of the result of Jones and Kok, obtained for constant Hamiltonians and orthogonal states [18].”
From Energy–time uncertainty relation for driven quantum systems (2013) · cites this paper as [18]
Citations
Cites
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
Probability theory the logic of science
Jaynes, E. T., & Bretthorst, G. L. (2003) · Cited by 4,600
Probability Theory: The Logic of Science
Jaynes, E. T. (2003) · doi:10.1017/cbo9780511790423 · Cited by 4,045
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776
Quantum-mechanical noise in an interferometer
Caves, C. M. (1981) · Physical Review D · doi:10.1103/physrevd.23.1693 · Cited by 3,202
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176
Quantum Detection and Estimation Theory
(1976) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6017-5 · Cited by 2,712
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440
Research works printed but not linked: 2
- L. Mandelstam, 1945, J. Phys. (USSR), 9, 249
- J. Uffink, 1994, Proceedings of the Third International Workshop on Squeezed States and Uncertainty Relations
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“(12) of a qubit held by Bob in a non-inertial frame.”
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O’Connor, E., Guarnieri, G., & Campbell, S. (2021) · Physical Review A · doi:10.1103/physreva.103.022210 · Cited by 67
“[35] P.”
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Argon, A. S. (2013) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2013.798049 · Cited by 57
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“See also [32, 33] for alternative derivations of the estimate (71).”
BackgroundGeometric quantum speed limits for Markovian dynamics in open quantum systems
Lan, K., Xie, S., & Cai, X.-J. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac696b · Cited by 29
In search of lost time: attosecond physics, petahertz optoelectronics, and quantum speed limit
Zheltikov, A. M. (2020) · Physics-Uspekhi · doi:10.3367/ufne.2020.11.038884 · Cited by 26
Quantum coherence and speed limit in the mean-field Dicke model of superradiance
Rossatto, D. Z., Pires, D. P., de Paula, F. M., & Neto, O. P. D. S. (2020) · Physical Review A · doi:10.1103/physreva.102.053716 · Cited by 25
“[74–88].”
Landauer principle and thermodynamics of computation
Chattopadhyay, P., Misra, A., Pandit, T., & Paul, G. (2025) · Reports on Progress in Physics · doi:10.1088/1361-6633/add6b3 · Cited by 33
Speed limits on correlations in bipartite quantum systems
Pandey, V., Shrimali, D., Mohan, B., Das, S., & Pati, A. K. (2023) · Physical Review A · doi:10.1103/physreva.107.052419 · Cited by 29
Speed limit of quantum metrology
Maleki, Y., Ahansaz, B., & Maleki, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-39082-w · Cited by 23
Dependence of the quantum speed limit on system size and control complexity
Lee, J., Arenz, C., RABITZ, H. A., & Russell, B. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aac6f3 · Cited by 22
Quantum speed limit based on the bound of Bures angle
Wu, S.-X., & Yu, C.-S. (2020) · Scientific Reports · doi:10.1038/s41598-020-62409-w · Cited by 21
Song, Y., & Kuang, L. (2019) · Annalen der Physik · doi:10.1002/andp.201800423 · Cited by 19
Cafaro, C., & Alsing, P. M. (2018) · Physical review. E · doi:10.1103/physreve.97.042110 · Cited by 19
“In the latter case, as mentioned earlier, the Fisher information plays a key role in the geometric interpretation of quantum speed limits of dynamical evolutions in quantum computing based on the notion of statistical distance between quantum states, either pure or mixed [25, 26].”
BackgroundGeneralised quantum speed limit for arbitrary time-continuous evolution
Thakuria, D., Srivastav, A., Mohan, B., Kumari, A., & Pati, A. K. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad15ad · Cited by 24
Control of quantum dynamics: Non-Markovianity and the speedup of the open system evolution
Zhang, Y.-J., Xia, Y., & Fan, H. (2016) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/116/30001 · Cited by 18
Quantum speed limit for robust state characterization and engineering
Kobayashi, K., & Yamamoto, N. (2020) · Physical Review A · doi:10.1103/physreva.102.042606 · Cited by 17
“[3] P.”
Detecting quantum speedup in closed and open systems
Xu, Z.-Y. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/7/073005 · Cited by 18
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
“There is a geometric derivation of the ML bound [13].”
BackgroundMethodResultTime-limited optimal dynamics beyond the quantum speed limit
Gajdacz, M., Das, K. K., Arlt, J., Sherson, J. F., & Opatrný, T. (2015) · Physical Review A · doi:10.1103/physreva.92.062106 · Cited by 14
Shrimali, D., Panda, B., & Pati, A. K. (2024) · Physical Review A · doi:10.1103/physreva.110.022425 · Cited by 13
Quantum Speed Limit for States and Observables of Perturbed Open Systems
Yadin, B., Imai, S., & Gühne, O. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.230404 · Cited by 14
“We now have extensions to mixed states and driven and open systems [3–7], and an understanding of the connection to the geometry of quantum state spaces [8–10].”
BackgroundSpeed limit for open systems coupled to general environments
Shiraishi, N., & Saito, K. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.023074 · Cited by 13
“These relations originated from the uncertainty relation between time and energy; hence, the operation time is inevitably accompanied by quantities on energy [1, 3–10].”
BackgroundSpeedup of quantum evolution of multiqubit entanglement states
Zhang, Y.-J., Han, W., Xia, Y., Tian, J., & Fan, H. (2016) · Scientific Reports · doi:10.1038/srep27349 · Cited by 13
Relativistic quantum speed limit time in dephasing noise
Khan, S., & Khan, N. A. (2015) · The European Physical Journal Plus · doi:10.1140/epjp/i2015-15216-0 · Cited by 11
Ohmic reservoir-based non-Markovianity and Quantum Speed Limit Time
Zou, H.-M., Liu, R., Long, D., Yang, J., & Lin, D. (2020) · Physica Scripta · doi:10.1088/1402-4896/aba2b5 · Cited by 12
Quantum speed limit in terms of coherence variations
Mai, Z.-Y., & Yu, C. (2024) · Physical Review A · doi:10.1103/physreva.110.042425 · Cited by 12
“Up to now, QSL has attracted increasing interest and has been generalized in different scenarios [4, 5] including the QSLs for the mixed states [6, 7], time-dependent Hamiltonian [8, 9], the geometric understandings [10– 12] and so on [13].”
Quantum speed limit of a noisy continuous-variable system
Wu, W., & An, J. (2022) · Physical Review A · doi:10.1103/physreva.106.062438 · Cited by 11
“Later, Margolus and Levitin provided an alternative QSL time in terms of the energy difference τML = π~/(2〈Ĥ〉) [6, 7].”
BackgroundDynamical decoupling assisted acceleration of two-spin evolution in XY spin-chain environment
Wei, Y.-B., Zou, J., Wang, Z.-M., Shao, B., & Li, H. (2015) · Physics Letters A · doi:10.1016/j.physleta.2015.11.013 · Cited by 11
Quantum speed limit of Jaynes-Cummings model with detuning for arbitrary initial states
Shahri, Y., Hadipour, M., Haddadi, S., Dolatkhah, H., & Haseli, S. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.128783 · Cited by 11
Environment-assisted non-Markovian speedup dynamics control
Xu, K. D., Han, W., Zhang, Y., Xia, Y., & Fan, H. (2017) · Annals of Physics · doi:10.1016/j.aop.2017.10.017 · Cited by 11
Classical and quantum speed limits
Bolonek-Lasoń, K., Gonera, J., & Kosiński, P. (2021) · Quantum · doi:10.22331/q-2021-06-24-482 · Cited by 9
Quantum Speed Limit for a Moving Qubit inside a Leaky Cavity
Hadipour, M., Haseli, S., Dolatkhah, H., Haddadi, S., & Czerwiński, A. (2022) · Photonics · doi:10.3390/photonics9110875 · Cited by 10
Hamazaki, R. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013018 · Cited by 10
Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables
Zwierz, M., Pérez-Delgado, C. A., & Kok, P. (2010) · Physical Review A · doi:10.1103/physreva.82.042320 · Cited by 9
Self-citationXing, H., & Fu, L. (2020) · Physical Review A · doi:10.1103/physreva.102.062613 · Cited by 9
Quantum speed limits based on Schatten norms: Universality and tightness
Rosal, A. J. B., Soares-Pinto, D. O., & Pires, D. P. (2025) · Physics Letters A · doi:10.1016/j.physleta.2025.130250 · Cited by 10
“[ 42, 50, 62].”
Nishiyama, T., & Hasegawa, Y. (2025) · Physical Review A · doi:10.1103/physreva.111.012214 · Cited by 8
“Therefore, we introduce the normalized vector as follows: where ∥ | ψ ( t ) ⟩ ∥ ≡ ⟨ ψ ( t ) | ψ ( t ) ⟩ .”
Unitary evolution and the distinguishability of quantum states
Morley-Short, S., Rosenfeld, L. M., & Kok, P. (2014) · Physical Review A · doi:10.1103/physreva.90.062116 · Cited by 8
Self-citationQuantum speedup in noninertial frames
Xu, K. D., Zhu, H., Zhang, G., Wang, J., & Liu, W. (2020) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-8048-x · Cited by 8
Quantum speed limit with forbidden speed intervals
Chau, H. F. (2013) · Physical Review A · doi:10.1103/physreva.87.052142 · Cited by 8
Quantum speed limits for Bell-diagonal states
Han, W., Jiang, K.-X., Zhang, Y.-J., & Xia, Y. (2015) · Chinese Physics B · doi:10.1088/1674-1056/24/12/120304 · Cited by 8
Instantaneous angular velocity of quantum evolution
Huang, J., Hu, L., & Liu, F.-Y. (2020) · Physical Review A · doi:10.1103/physreva.102.062221 · Cited by 7
Gravitational Field effects on the Decoherence Process and the Quantum Speed Limit
Dehdashti, S., Avazzadeh, Z., Xu, Z., Shen, J. Q., Mirza, B., & Wang, H. (2017) · Scientific Reports · doi:10.1038/s41598-017-15114-0 · Cited by 7
“ds c B r dt B r dr r d d ( ) ( ) ( sin ), (8) 2 2 2 1 2 2 2 2 2 θ θ φ = − + + + −”
Quantum speed of evolution in a Markovian bosonic environment
Marian, P., & Marian, T. A. (2021) · Physical Review A · doi:10.1103/physreva.103.022221 · Cited by 7
“[24, 25] are derived as upper bounds on the rate of change of a distance-type measure of distinguishability.”
BackgroundEntanglement-assisted quantum speedup: Beating local quantum speed limits
Yasmin, F., & Sperling, J. (2024) · Physical Review A · doi:10.1103/physreva.110.012424 · Cited by 6
Excitation of time-dependent quantum systems: An application of time–energy uncertainty relations
Khalil, T., & Richert, J. (2014) · Physica B Condensed Matter · doi:10.1016/j.physb.2014.09.027 · Cited by 5
Margolus–Levitin speed limit across quantum to classical regimes based on trace distance*
Wu, S.-X., & Yu, C.-S. (2020) · Chinese Physics B · doi:10.1088/1674-1056/ab7dab · Cited by 6
Russell, B., & Stepney, S. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-39074-6_19 · Cited by 6
Controlling the quantum speed limit time for unital maps via filtering operations
Haseli, S., & Salimi, S. (2020) · Laser Physics Letters · doi:10.1088/1612-202x/abac15 · Cited by 6
Non-Markovian speedup dynamics control of the damped Jaynes–Cummings model with detuning
Xu, K. D., Han, W., Zhang, Y.-J., & Fan, H. (2018) · Chinese Physics B · doi:10.1088/1674-1056/27/1/010302 · Cited by 6
State preparation in a Jaynes-Cummings lattice with quantum optimal control
Parajuli, P., Govindarajan, A., & Tian, L. (2023) · Scientific Reports · doi:10.1038/s41598-023-47002-1 · Cited by 5
“Also, � E ave = 1 T (cid:31) T 0 dt � E ( t ) is the average energy fluctuation during the time evolution with � E ( t ) = �[ H t − � H t �] 2 � being the instantaneous energy fluctuation of the Hamiltonian H t at time t , and the operator average is taken on the instantaneous quantum state | ψ( t…”
BackgroundInfluentialQuantum geometry in many-body systems with precursors of criticality
Střeleček, J., & Cejnar, P. (2025) · Physical Review A · doi:10.1103/physreva.111.012211 · Cited by 5
Non-monotonicity of Trace Distance Under Tensor Products
Maziero, J. (2015) · Brazilian Journal of Physics · doi:10.1007/s13538-015-0350-y · Cited by 5
“ancemeasuresin D(H) naturallyappear also in the contexts of quantum foundations [7,8, 9], quantum processes [10,11], quantum cryptography [12,13], quantum phase transitions [14], quantum speed limits [15,16,17,18,19,20], quantum channel capacities [21], and also in the theories of quantum entanglement [22,23], quantum…”
BackgroundQuantum speed limits of a qubit system interacting with a nonequilibrium environment
He, Z., Yao, C., Li, L., & Wang, Q. (2016) · Chinese Physics B · doi:10.1088/1674-1056/25/8/080304 · Cited by 5
Coherent-driving-assisted quantum speedup in Markovian channels*
Lu, X., Zhang, Y., & Xia, Y. (2020) · Chinese Physics B · doi:10.1088/1674-1056/abc150 · Cited by 5
Quantum speed limit for mixed states in a unitary system
Huang, J., Qin, L., Chen, G.-L., Hu, L., & Liu, F.-Y. (2022) · Chinese Physics B · doi:10.1088/1674-1056/ac76b4 · Cited by 5
Quantum acceleration by an ancillary system in non-Markovian environments
Fan, J., Wu, S.-X., & Yu, C. (2021) · Quantum Information Processing · doi:10.1007/s11128-020-02964-3 · Cited by 5
Quantum speed limit for the maximum coherent state under the squeezed environment*
Du, K.-Y., Ma, Y.-J., Wu, S.-X., & Yu, C. (2021) · Chinese Physics B · doi:10.1088/1674-1056/ac0daf · Cited by 5
Metadata
- Authors
- Jones, P. J., & Kok, P.
- Affiliations
- University of Sheffield (GB)
- ORCID
- Kok, Pieter
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2010-08-16
- Volume
- 82
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2008738328
- Cited by
- 172
- References
- 29
- Citations by year
- 2026: 6 · 2025: 22 · 2024: 14 · 2023: 12 · 2022: 15 · 2021: 13 · 2020: 17 · 2019: 6 · 2018: 7 · 2017: 7 · 2016: 11 · 2015: 14 · 2014: 12 · 2013: 9 · 2012: 2
- FWCI
- 2.74
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum speed limit, statistical distance, quantum states, unitary evolution, mixed states, completely positive trace-preserving maps, non-unitary evolution, counterexample
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