Quantum speed limit

In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable states.[1] QSL 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]

In 2017, QSLs were studied in a quantum oscillator at high temperature. [8] In 2018, it was shown that QSL are not restricted to the quantum domain and that similar bounds hold in classical systems. [9][10] QSL have been used to explore the limits of computation[11][12] and complexity.

References
  1. 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. doi:10.1088/1751-8121/aa86c6.
  2. Mandelshtam, L. I.; Tamm, I. E. (1945). "The uncertainty relation between energy and time in nonrelativistic quantum mechanics". J. Phys. (USSR). 9: 249–254.
  3. 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. doi:10.1016/S0167-2789(98)00054-2.
  4. 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. doi:10.1103/PhysRevLett.110.050402. PMID 23414007.
  5. 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. doi:10.1103/PhysRevLett.110.050403. PMID 23414008.
  6. Deffner, S.; Lutz, E. (3 July 2013). "Quantum speed limit for non-Markovian dynamics". Physical Review Letters. 111 (1): 010402. arXiv:1302.5069. doi:10.1103/PhysRevLett.111.010402.
  7. Cimmarusti, A. D.; Yan, Z.; Patterson, B. D.; Corcos, L. P.; Orozco, L. A.; Deffner, S. (11 June 2015). "Quantum speed limit for non-Markovian dynamics". Physical Review Letters. 114 (23): 233602. arXiv:1503.02591. doi:10.1103/PhysRevLett.114.233602.
  8. Deffner, S. (20 October 2017). "Geometric quantum speed limits: a case for Wigner phase space". New Journal of Physics. 19 (10): 103018. doi:10.1088/1367-2630/aa83dc.
  9. 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). doi:10.1103/PhysRevLett.120.070401. PMID 29542956.
  10. Okuyama, Manaka; Ohzeki, Masayuki (12 February 2018). "Quantum Speed Limit is Not Quantum". Physical Review Letters. 120 (7): 070402. arXiv:1710.03498. doi:10.1103/PhysRevLett.120.070402. PMID 29542975.
  11. Lloyd, Seth (31 August 2000). "Ultimate physical limits to computation". Nature. 406 (6799): 1047–1054. arXiv:quant-ph/9908043. doi:10.1038/35023282. ISSN 1476-4687. PMID 10984064.
  12. Lloyd, Seth (24 May 2002). "Computational Capacity of the Universe". Physical Review Letters. 88 (23): 237901. arXiv:quant-ph/0110141. doi:10.1103/PhysRevLett.88.237901. PMID 12059399.
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