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.
 M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, Phys. Rev. Lett. 110, 050402 (2013).
 A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, Phys. Rev. Lett. 110, 050403 (2013).
 S. Deffner and E. Lutz, Phys. Rev. Lett. 111, 010402 (2013).
 A. Carlini, A. Hosoya, T. Koike, and Y. Okudaira, J. Phys. A: Math. Theor. 41, 045303 (2008).
 B. Russell and S. Stepney, J. Phys. A: Math. Theor. 48, 115303 (2015).
 D. C. Brody and D. M. Meier, Phys. Rev. Lett. 114, 100502 (2015).
 D. C. Brody, G. W. Gibbons, and D. M. Meier, New J. Phys. 17, 033048 (2015).
 X. Wang, M. Allegra, K. Jacobs, S. Lloyd, C. Lupo, and M. Mohseni, Phys. Rev. Lett. 114, 170501 (2015).
 J. Geng, Y. Wu, X. Wang, K. Xu, F. Shi, Y. Xie, X. Rong, and J. Du, Phys. Rev. Lett. 117, 170501 (2016).
 F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17, 075015 (2015).
 F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, Phys. Rev. Lett. 118, 150601 (2017).
 S. Julià-Farré, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Phys. Rev. Research 2, 023113 (2020).
 A. Arvanitoyeorgos, An introduction to Lie groups and the geometry homogeneous spaces, Student Mathematical Library 22, American Mathematical Society 2003.
 S. Kobayashi and K. Nomizu, Foundations of Differential Geometry Vol. I,II, Whiley Classics Library, John Wiley & Sons 1996.
 O. Andersson and H. Heydari, J. Phys. A: Math. Theor. 47, 215301 (2014).
 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.
 G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Phys. Rev. Lett. 125, 180603 (2020).
 R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, Mathematical Surveys and Monographs 91, American Mathematical Society 2002.
 Akram Touil, Barış Çakmak, and Sebastian Deffner, "Ergotropy from quantum and classical correlations", Journal of Physics A: Mathematical and Theoretical 55 2, 025301 (2022).
 Sebastian Deffner, "Quantum speed-limited depletion of physical resources", Quantum Views 5, 55 (2021).
 Maxwell Aifer and Sebastian Deffner, "From quantum speed limits to energy-efficient quantum gates", New Journal of Physics 24 5, 055002 (2022).
The above citations are from Crossref's cited-by service (last updated successfully 2022-12-08 12:48:01) and SAO/NASA ADS (last updated successfully 2022-12-08 12:48:02). 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.