Time-optimal quantum transformations with bounded bandwidth
Fysikum, Stockholms universitet, 106 91 Stockholm, Sweden
Published: | 2021-05-27, volume 5, page 462 |
Eprint: | arXiv:2011.11963v3 |
Doi: | https://doi.org/10.22331/q-2021-05-27-462 |
Citation: | Quantum 5, 462 (2021). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is initially in an incoherent state relative to the observable and that the state evolves according to a von Neumann equation with a Hamiltonian whose bandwidth is uniformly bounded. The transformation time depends intricately on the observable's and the initial state's eigenvalue spectrum and the relative constellation of the associated eigenspaces. The problem of finding quantum speed limits consequently divides into different cases requiring different strategies. We derive quantum speed limits in a large number of cases, and we simultaneously develop a method to break down complex cases into manageable ones. The derivations involve both combinatorial and differential geometric techniques. We also study multipartite systems and show that allowing correlations between the parts can speed up the transformation time. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.
► BibTeX data
► References
[1] M. R. Frey, Quantum Inf. Process. 15, 3919 (2016).
https://doi.org/10.1007/s11128-016-1405-x
[2] S. Deffner and S. Campbell, J. Phys. A: Math. Theor. 50, 453001 (2017).
https://doi.org/10.1088/1751-8121/aa86c6
[3] M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, Phys. Rev. Lett. 110, 050402 (2013).
https://doi.org/10.1103/PhysRevLett.110.050402
[4] A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Phys. Rev. Lett. 110, 050403 (2013).
https://doi.org/10.1103/PhysRevLett.110.050403
[5] Y-J. Zhang, W. Han, Y-J. Xia, J-P. Cao, and H. Fan, Scientific Reports 4, 4890 (2014).
https://doi.org/10.1038/srep04890
[6] S. Deffner and E. Lutz, Phys. Rev. Lett. 111, 010402 (2013).
https://doi.org/10.1103/PhysRevLett.111.010402
[7] D. P. Pires, M. Cianciaruso, L. C. Céleri, G. Adesso, and D. O. Soares-Pinto, Phys. Rev. X 6, 021031 (2016).
https://doi.org/10.1103/PhysRevX.6.021031
[8] A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira, Phys. Rev. Lett. 96, 060503 (2006).
https://doi.org/10.1103/PhysRevLett.96.060503
[9] A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira, Phys. Rev. A 75, 042308 (2007).
https://doi.org/10.1103/PhysRevA.75.042308
[10] A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira, J. Phys. A: Math. Theor. 41, 045303 (2008).
https://doi.org/10.1088/1751-8113/41/4/045303
[11] B. Russell and S. Stepney, Phys. Rev. A 90, 012303 (2014).
https://doi.org/10.1103/PhysRevA.90.012303
[12] B. Russell and S. Stepney, J. Phys. A: Math. Theor. 48, 115303 (2015).
https://doi.org/10.1088/1751-8113/48/11/115303
[13] D. C. Brody and D. M. Meier, Phys. Rev. Lett. 114, 100502 (2015).
https://doi.org/10.1103/PhysRevLett.114.100502
[14] D. C. Brody, G. W. Gibbons, and D. M. Meier, New J. Phys. 17, 033048 (2015).
https://doi.org/10.1088/1367-2630/17/3/033048
[15] X. Wang, M. Allegra, K. Jacobs, S. Lloyd, C. Lupo, and M. Mohseni, Phys. Rev. Lett. 114, 170501 (2015).
https://doi.org/10.1103/PhysRevLett.114.170501
[16] J. Geng, Y. Wu, X. Wang, K. Xu, F. Shi, Y. Xie, X. Rong, and J. Du, Phys. Rev. Lett. 117, 170501 (2016).
https://doi.org/10.1103/PhysRevLett.117.170501
[17] H. Wakamura and T. Koike, New J. Phys. 22, 073010 (2020).
https://doi.org/10.1088/1367-2630/ab8ab3
[18] W. Pusz and S. L. Woronowicz, Comm. Math. Phys. 58, 273 (1978).
https://doi.org/10.1007/BF01614224
[19] A. Lenard, J. Stat. Phys. 19, 6 (1978).
https://doi.org/10.1007/BF01011769
[20] P. Skrzypczyk, R. Silva, and N. Brunner, Phys. Rev. E 91, 052133 (2015).
https://doi.org/10.1103/PhysRevE.91.052133
[21] A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, Europhysics Letters (EPL) 67, 565 (2004).
https://doi.org/10.1209/epl/i2004-10101-2
[22] R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013).
https://doi.org/10.1103/PhysRevE.87.042123
[23] F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17, 075015 (2015).
https://doi.org/10.1088/1367-2630/17/7/075015
[24] F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Phys. Rev. Lett. 118, 150601 (2017).
https://doi.org/10.1103/PhysRevLett.118.150601
[25] S. Julià-Farré, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Phys. Rev. Research 2, 023113 (2020).
https://doi.org/10.1103/PhysRevResearch.2.023113
[26] T. Sakai, Riemannian Geometry, Translations of Mathematical Monographs 149, American Mathematical Society 1996.
https://doi.org/10.1090/mmono/149
[27] A. Arvanitoyeorgos, An introduction to Lie groups and the geometry homogeneous spaces, Student Mathematical Library 22, American Mathematical Society 2003.
[28] S. Lang, Algebra, Third Ed., Addison-Wesley Publishing Company 1993.
https://doi.org/10.1007/978-1-4613-0041-0
[29] L. Gurvits and H. Barnum, Phys. Rev. A 66, 062311 (2002).
https://doi.org/10.1103/PhysRevA.66.062311
[30] L. Gurvits and H. Barnum, Phys. Rev. A 68, 042312 (2003).
https://doi.org/10.1103/PhysRevA.68.042312
[31] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry Vol. I,II, Whiley Classics Library, John Wiley & Sons 1996.
[32] O. Andersson and H. Heydari, J. Phys. A: Math. Theor. 47, 215301 (2014).
https://doi.org/10.1088/1751-8113/47/21/215301
[33] O. Andersson, Holonomy in quantum information geometry, Thesis, arXiv:1910.08140.
arXiv:1910.08140
[34] A. Edelman, T. A. Arias, and S. T. Smith, Siam J. Matrix Anal. Appl. 20, 303 (1998).
https://doi.org/10.1137/S0895479895290954
[35] X. Ma, M. Kirby, and C. Peterson, The flag manifold as a tool for analyzing and comparing data sets, arXiv:2006.14086.
arXiv:2006.14086
[36] F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Eds.), Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics 195, Springer 2019.
https://doi.org/10.1007/978-3-319-99046-0
[37] G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Phys. Rev. Lett. 125, 180603 (2020).
https://doi.org/10.1103/PhysRevLett.125.180603
[38] R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, Mathematical Surveys and Monographs 91, American Mathematical Society 2002.
https://doi.org/10.1090/surv/091
Cited by
[1] Niklas Hörnedal and Ole Sönnerborn, "Tight lower bounds on the time it takes to generate a geometric phase", Physica Scripta 98 10, 105108 (2023).
[2] Akram Touil, Barış Çakmak, and Sebastian Deffner, "Ergotropy from quantum and classical correlations", Journal of Physics A: Mathematical and Theoretical 55 2, 025301 (2022).
[3] Sebastian Deffner, "Quantum speed-limited depletion of physical resources", Quantum Views 5, 55 (2021).
[4] Maxwell Aifer and Sebastian Deffner, "From quantum speed limits to energy-efficient quantum gates", New Journal of Physics 24 5, 055002 (2022).
[5] Nikolai Il'in and Oleg Lychkovskiy, "Quantum speed limit for thermal states", Physical Review A 103 6, 062204 (2021).
[6] Nikolai Il`in and Oleg Lychkovskiy, "Quantum speed limit for thermal states", arXiv:2005.06416, (2020).
The above citations are from Crossref's cited-by service (last updated successfully 2023-11-29 13:07:41) and SAO/NASA ADS (last updated successfully 2023-11-29 13:07:42). The list may be incomplete as not all publishers provide suitable and complete citation data.
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.
Pingback: Perspective in Quantum Views by Sebastian Deffner "Quantum speed-limited depletion of physical resources"