Classical and quantum speed limits

Katarzyna Bolonek-Lasoń1, Joanna Gonera2, and Piotr Kosiński2

1Department of Statistical Methods, Faculty of Economics and Sociology University of Lodz, 41/43 Rewolucji 1905 St., 90-214 Lodz, Poland
2Department of Computer Science, Faculty of Physics and Applied Informatics University of Lodz, 149/153 Pomorska St., 90-236 Lodz, Poland

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The new bound on quantum speed limit (in terms of relative purity) is derived by applying the original Mandelstam-Tamm one to the evolution in the space of Hilbert-Schmidt operators acting in the initial space of states. It is shown that it provides the quantum counterpart of the classical speed limit derived in $\textit{Phys. Rev. Lett. 120 (2018), 070402}$ and the $\hbar\rightarrow 0$ limit of the former yields the latter. The existence of classical limit is related to the degree of mixing of the quantum state.

► BibTeX data

► References

[1] L. Mandelstam, I. Tamm, Journ. Phys 9, 249 (1945).
https:/​/​doi.org/​10.1007/​978-3-642-74626-0_8

[2] N. Margolus, L.B. Levitin, Physica D120, 188 (1998).
https:/​/​doi.org/​10.1016/​S0167-2789(98)00054-2

[3] L.B. Levitin, T. Toffoli, Phys. Rev. Lett. 103, 160502 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.160502

[4] G.N. Fleming, Nuovo Cim. 16A, 232 (1973).
https:/​/​doi.org/​10.1007/​BF02819419

[5] W. Wootters, Phys. Rev. D23, 357 (1981).
https:/​/​doi.org/​10.1103/​PhysRevD.23.357

[6] K. Bhattacharyya, Journ. Phys. A16, 2993 (1983).
https:/​/​doi.org/​10.1088/​0305-4470/​16/​13/​021

[7] J. Anandan, Y. Aharonov, Phys. Rev. Lett. 65, 1697 (1990).
https:/​/​doi.org/​10.1103/​PhysRevLett.65.1697

[8] L. Vaidman, Am. Journ. Phys. 60, 182 (1992).
https:/​/​doi.org/​10.1119/​1.16940

[9] A. Uhlmann, Phys. Lett. A161, 329 (1992).
https:/​/​doi.org/​10.1016/​0375-9601(92)90555-Z

[10] P. Pfeifer, Phys. Rev. Lett. 70, 3365 (1993).
https:/​/​doi.org/​10.1103/​PhysRevLett.70.3365

[11] S. Lloyd, Phys. Rev. Lett. 88, 237901 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.88.237901

[12] V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. A67, 052109 (2003).
https:/​/​doi.org/​10.1103/​PhysRevA.67.052109

[13] P. Kosiński, M. Zych, Phys. Rev. A73, 024303 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.024303

[14] B. Zieliński, M. Zych, Phys. Rev. A74, 034301 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.74.034301

[15] T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, G. Santoro, Phys. Rev. Lett. 103, 240501 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.240501

[16] A. Mostafazadeh, Phys. Rev. A79, 014101 (2009).
https:/​/​doi.org/​10.1103/​PhysRevA.79.014101

[17] P. Jones, P. Kok, Phys. Rev. A82, 022107 (2010).
https:/​/​doi.org/​10.1103/​PhysRevA.82.022107

[18] A. del Campo, M. Rams, W. Zurek, Phys. Rev. Lett. 109, 115703 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.115703

[19] R. Demkowicz-Dobrzański, J. Kolodynski, M. Guta, Nat. Commun. 3, 1063 (2012).
https:/​/​doi.org/​10.1038/​ncomms2067

[20] M. Taddei, B. Fisher, L. Davidovich, R. de Matos Filho, Phys. Rev. Lett. 110, 050402 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.050402

[21] A. del Campo, I. Egusquiza, M. Plenio, S. Huelga, Phys. Rev. Lett. 110, 050403 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.050403

[22] S. Deffner, E. Lutz, Phys. Rev. Lett. 111, 010402 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.111.010402

[23] P. Poggi, F. Lombardo, D. Wisniacki, Europhys. Lett. 104, 40005 (2013).
https:/​/​doi.org/​10.1209/​0295-5075/​104/​40005

[24] R. Uzdin, E. Lutz, R. Kosloff, Purity and entropy evolution speed limits for open quantum systems, arXiv: 1408.1227.
arXiv:1408.1227

[25] Z.-Y. Xu, S. Luo, W.L. Wang, C. Liu, S. Zhu, Phys. Rev. A89, 012307 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.89.012307

[26] Y.-J. Zhang, W. Han, Y.-J. Xia, J.-P. Cao, H. Fan, Sci. Rep 4, 4890 (2014).
https:/​/​doi.org/​10.1038/​srep04890

[27] Z. Sun, J. Liu, J. Ma, X. Wang, Scientific Reports 5, 8444 (2015).
https:/​/​doi.org/​10.1038/​srep08444

[28] S.-X. Wu, Y. Zhang, C. Yu, H. Song, Journ. Phys. A48,045301 (2015).
https:/​/​doi.org/​10.1088/​1751-8113/​48/​4/​045301

[29] I. Marvian, D. Lidar, Phys. Rev. Lett. 115, 210402 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.210402

[30] D. Mondal, C. Datta, Sk Sazim, Phys. Lett. A380, 689 (2015).
https:/​/​doi.org/​10.1016/​j.physleta.2015.12.015

[31] R. Uzdin, R. Kosloff, Europh. Lett. 115, 40003 (2016).
https:/​/​doi.org/​10.1209/​0295-5075/​115/​40003

[32] I. Marivan, R. Spekkens, P. Zanardi, Phys. Rev. A93, 052331 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.93.052331

[33] D. Pires, M. Cianciaruso, L. Celeri, G. Adesso, Phys. Rev. X6, 021031 (2016).
https:/​/​doi.org/​10.1103/​PhysRevX.6.021031

[34] S. Campbell, S. Deffner, Phys. Rev. Lett. 118, 100601 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.118.100601

[35] A. del Campo, J. Molina-Vilaplana, J. Sonner, Phys. Rev. D95, 126008 (2017).
https:/​/​doi.org/​10.1103/​PhysRevD.95.126008

[36] S. Deffner, S. Campbell, Journ. Phys. A50, 453001 (2017).
https:/​/​doi.org/​10.1088/​1751-8121/​aa86c6

[37] S. Deffner, New Journ. Phys. 19, 103018 (2017).
https:/​/​doi.org/​10.1088/​1367-2630/​aa83dc

[38] M. Cianciaruso, S. Maniscalco, G. Adesso, Phys. Rev. A96, 012105 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.96.012105

[39] X. Cai, Y. Zheng, Phys. Rev. A95, 052104 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.95.052104

[40] F. Campaioli, F. Pollock, F. Binder, K. Modi, Phys. Rev. Lett. 120, 060409 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.060409

[41] S. Ito, Phys. Rev. Lett. 121, 030605 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.030605

[42] F. Campaioli, F. Pollock, K. Modi, Quantum 3, 168 (2019).
https:/​/​doi.org/​10.22331/​q-2019-08-05-168

[43] J. Teittinen, H. Lyyra, S. Maniscalco, New Journ. Phys. 21, 123041 (2019).
https:/​/​doi.org/​10.1088/​1367-2630/​ab59fe

[44] S. Sun, Y. Zheng, Phys. Rev. Lett. 123, 180403 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.180403

[45] A. Diaz, V. Martikyan, S. Glaser, D. Sugny, Phys. Rev. A102, 033104 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.102.033104

[46] T. Fogarty, S. Deffner, T. Bush, S. Campbell, Phys. Rev. Lett. 124, 110601 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.110601

[47] E. O'Connor, G. Guarnieri, S. Campbell, Phys. Rev. A103, 022210 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.022210

[48] J. Teittinen, S. Maniscalco, Entropy 23, 331 (2021).
https:/​/​doi.org/​10.3390/​e23030331

[49] B. Shanahan, A. Chenu, N. Margolus, A. del Campo, Phys. Rev. Lett. 120, 070401 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.070401

[50] M. Okuyama, M. Ohzeki, Phys. Rev. Lett. 120, 070402 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.070402

[51] N. Shiraishi, K. Funo, K. Saito, Phys. Rev. Lett. 121, 070601 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.070601

[52] K. Funo, N. Shiraishi, K. Saito, New Journ. Phys. 21, 013006 (2019).
https:/​/​doi.org/​10.1088/​1367-2630/​aaf9f5

[53] V.T. Vo, T.V. Vu, Y. Hasegawa, Phys. Rev. E102, 062132 (2020).
https:/​/​doi.org/​10.1103/​PhysRevE.102.062132

[54] S.-X. Wu, C.-S. Yu, Chin. Phys. B29, 050302 (2020).
https:/​/​doi.org/​10.1088/​1674-1056/​ab7dab

[55] S. Nicholson, L. Garcia-Pintos, A. del Campo, J. Green, Nature Physics 16, 1211 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0981-y

[56] K. Audenaert, Quant. Inf. Comp. 14, 31 (2014).
https:/​/​doi.org/​10.26421/​QIC14.1-2-2

[57] M. Frey, Quant. Inf. Process 15, 3919 (2016).
https:/​/​doi.org/​10.1007/​s11128-016-1405-x

[58] I. Bengtsson, K. Życzkowski, Geometry of quantum states: an introduction to quantum entanglement, Cambridge University Press (2008).
https:/​/​doi.org/​10.1017/​CBO9780511535048

[59] N. Mukunda, Pramana 11, 1 (1978).
https:/​/​www.ias.ac.in/​article/​fulltext/​pram/​011/​01/​0001-0015

[60] J. Moyal, M. Bartlett, Math. Proc. Cambridge Math. Soc. 45, 99 (1949).
https:/​/​doi.org/​10.1017/​S0305004100000487

[61] C. Zachos, D. Fairlie, T. Curtright, Quantum Mechanics in Phase Space, World Scientific (2005).
https:/​/​www.worldscientific.com/​doi/​pdf/​10.1142/​9789812703507_fmatter

Cited by

[1] Carlo Cafaro and Paul M. Alsing, "Complexity of pure and mixed qubit geodesic paths on curved manifolds", Physical Review D 106 9, 096004 (2022).

[2] Weiquan Meng and Zhenyu Xu, "Quantum speed limits in arbitrary phase spaces", Physical Review A 107 2, 022212 (2023).

[3] Tan Van Vu and Keiji Saito, "Topological Speed Limit", Physical Review Letters 130 1, 010402 (2023).

[4] Pablo M. Poggi, Steve Campbell, and Sebastian Deffner, "Diverging Quantum Speed Limits: A Herald of Classicality", PRX Quantum 2 4, 040349 (2021).

[5] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", EPJ Quantum Technology 9 1, 19 (2022).

[6] Kang Lan, Shijie Xie, and Xiangji Cai, "Geometric quantum speed limits for Markovian dynamics in open quantum systems", New Journal of Physics 24 5, 055003 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-03-28 14:54:44). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2024-03-28 14:54:44).