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 $hbarrightarrow 0$ 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

@article{BolonekLason2021classicalquantum, doi = {10.22331/q-2021-06-24-482}, url = {https://doi.org/10.22331/q-2021-06-24-482}, title = {Classical and quantum speed limits}, author = {Bolonek-Laso{‘{n}}, Katarzyna and Gonera, Joanna and Kosi{‘{n}}ski, Piotr}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {5}, pages = {482}, month = jun, year = {2021}<br /> }

► 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

Could not fetch Crossref cited-by data during last attempt 2021-06-24 14:42:08: Could not fetch cited-by data for 10.22331/q-2021-06-24-482 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2021-06-24 14:42:09).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

Generative Data Intelligence

Abstract

► BibTeX data

► References

Cited by

Home

Home

Latest Intelligence

Homepage – Crowdfund Suite

Homepage – Crowdfund Suite

Understanding Google’s Perspective on 503 Status Codes

More Than 3× As Many Tesla Model Y Sales As Tesla Model 3 Sales In USA In 1st Quarter – CleanTechnica

Volkswagen Gets Critical Tech Boost in China from Xpeng – CleanTechnica

A studio helmed by StarCraft 2’s multiplayer lead wants to create an RTS ‘paradigm shift’ with its unannounced game

Chat with us