Limitation on the minimum time for a quantum system to evolve between two states
In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable (orthogonal) states.[1] QSL theorems are closely related to time-energy uncertainty relations. In 1945, Leonid Mandelstam and Igor Tamm derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion.[2] Over half a century later, Norman Margolus and Lev Levitin showed that the speed of evolution cannot exceed the mean energy,[3] a result known as the Margolus–Levitin theorem. Realistic physical systems in contact with an environment are known as open quantum systems and their evolution is also subject to QSL.[4][5] Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes,[6] which was verified in a cavity QED experiment.[7]
QSL have been used to explore the limits of computation[8][9] and complexity. In 2017, QSLs were studied in a quantum oscillator at high temperature.[10] In 2018, it was shown that QSL are not restricted to the quantum domain and that similar bounds hold in classical systems.[11][12] In 2021, both the Mandelstam-Tamm and the Margolus–Levitin QSL bounds were concurrently tested in a single experiment[13] which indicated there are "two different regimes: one where the Mandelstam-Tamm limit constrains the evolution at all times, and a second where a crossover to the Margolus-Levitin limit occurs at longer times."
^Deffner, S.; Campbell, S. (10 October 2017). "Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control". J. Phys. A: Math. Theor.50 (45): 453001. arXiv:1705.08023. Bibcode:2017JPhA...50S3001D. doi:10.1088/1751-8121/aa86c6. S2CID 3477317.
^Mandelshtam, L. I.; Tamm, I. E. (1945). "The uncertainty relation between energy and time in nonrelativistic quantum mechanics". J. Phys. (USSR). 9: 249–254. Reprinted as Mandelstam, L.; Tamm, Ig. (1991). "The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics". In Bolotovskii, Boris M.; Frenkel, Victor Ya.; Peierls, Rudolf (eds.). Selected Papers. Berlin, Heidelberg: Springer. pp. 115–123. doi:10.1007/978-3-642-74626-0_8. ISBN 978-3-642-74628-4. Retrieved 2024-04-06.
^Margolus, Norman; Levitin, Lev B. (September 1998). "The maximum speed of dynamical evolution". Physica D: Nonlinear Phenomena. 120 (1–2): 188–195. arXiv:quant-ph/9710043. Bibcode:1998PhyD..120..188M. doi:10.1016/S0167-2789(98)00054-2. S2CID 468290.
^Taddei, M. M.; Escher, B. M.; Davidovich, L.; de Matos Filho, R. L. (30 January 2013). "Quantum Speed Limit for Physical Processes". Physical Review Letters. 110 (5): 050402. arXiv:1209.0362. Bibcode:2013PhRvL.110e0402T. doi:10.1103/PhysRevLett.110.050402. PMID 23414007. S2CID 38373815.
^del Campo, A.; Egusquiza, I. L.; Plenio, M. B.; Huelga, S. F. (30 January 2013). "Quantum Speed Limits in Open System Dynamics". Physical Review Letters. 110 (5): 050403. arXiv:1209.1737. Bibcode:2013PhRvL.110e0403D. doi:10.1103/PhysRevLett.110.050403. PMID 23414008. S2CID 8362503.
^Deffner, S.; Lutz, E. (3 July 2013). "Quantum speed limit for non-Markovian dynamics". Physical Review Letters. 111 (1): 010402. arXiv:1302.5069. Bibcode:2013PhRvL.111a0402D. doi:10.1103/PhysRevLett.111.010402. PMID 23862985. S2CID 36711861.
^Cimmarusti, A. D.; Yan, Z.; Patterson, B. D.; Corcos, L. P.; Orozco, L. A.; Deffner, S. (11 June 2015). "Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics". Physical Review Letters. 114 (23): 233602. arXiv:1503.02591. Bibcode:2015PhRvL.114w3602C. doi:10.1103/PhysRevLett.114.233602. PMID 26196802. S2CID 14904633.
^Lloyd, Seth (24 May 2002). "Computational Capacity of the Universe". Physical Review Letters. 88 (23): 237901. arXiv:quant-ph/0110141. Bibcode:2002PhRvL..88w7901L. doi:10.1103/PhysRevLett.88.237901. PMID 12059399. S2CID 6341263.
^Deffner, S. (20 October 2017). "Geometric quantum speed limits: a case for Wigner phase space". New Journal of Physics. 19 (10): 103018. arXiv:1704.03357. Bibcode:2017NJPh...19j3018D. doi:10.1088/1367-2630/aa83dc. hdl:11603/19409.
^Shanahan, B.; Chenu, A.; Margolus, N.; del Campo, A. (12 February 2018). "Quantum Speed Limits across the Quantum-to-Classical Transition". Physical Review Letters. 120 (7): 070401. arXiv:1710.07335. Bibcode:2018PhRvL.120g0401S. doi:10.1103/PhysRevLett.120.070401. PMID 29542956.
^Okuyama, Manaka; Ohzeki, Masayuki (12 February 2018). "Quantum Speed Limit is Not Quantum". Physical Review Letters. 120 (7): 070402. arXiv:1710.03498. Bibcode:2018PhRvL.120g0402O. doi:10.1103/PhysRevLett.120.070402. PMID 29542975. S2CID 4027745.
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