Tight, robust, and feasible quantum speed limits for open dynamics

Francesco Campaioli, Felix A. Pollock, and Kavan Modi

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

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Starting from a geometric perspective, we derive a quantum speed limit for arbitrary open quantum evolution, which could be Markovian or non-Markovian, providing a fundamental bound on the time taken for the most general quantum dynamics. Our methods rely on measuring angles and distances between (mixed) states represented as generalized Bloch vectors. We study the properties of our bound and present its form for closed and open evolution, with the latter in both Lindblad form and in terms of a memory kernel. Our speed limit is provably robust under composition and mixing, features that largely improve the effectiveness of quantum speed limits for open evolution of mixed states. We also demonstrate that our bound is easier to compute and measure than other quantum speed limits for open evolution, and that it is tighter than the previous bounds for almost all open processes. Finally, we discuss the usefulness of quantum speed limits and their impact in current research.

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[1] L. Mandelstam and I. Tamm, ``The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics,'' in Sel. Pap. (Springer Berlin Heidelberg, Berlin, Heidelberg, 1945) pp. 115–123.

[2] N. Margolus and L. B. Levitin, ``The maximum speed of dynamical evolution,'' Phys. D Nonlinear Phenom. 120, 188 (1998).

[3] S. Deffner and E. Lutz, ``Energy–time uncertainty relation for driven quantum systems,'' J. Phys. A Math. Theor. 46, 335302 (2013a).

[4] S. Deffner and S. Campbell, ``Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control,'' J. Phys. A Math. Theor. 50, 453001 (2017).

[5] S. Lloyd, ``Ultimate physical limits to computation,'' Nature 406, 1047 (2000).

[6] V. Giovannetti, S. Lloyd, and L. Maccone, ``Quantum limits to dynamical evolution,'' Phys. Rev. A 67, 1 (2003).

[7] S. Alipour, M. Mehboudi, and A. T. Rezakhani, ``Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound,'' Phys. Rev. Lett. 112, 120405 (2014).

[8] V. Giovannetti, S. Lloyd, and L. Maccone, ``Advances in quantum metrology,'' Nat. Photonics 5, 222 (2011).

[9] A. W. Chin, S. F. Huelga, and M. B. Plenio, ``Quantum Metrology in Non-Markovian Environments,'' Phys. Rev. Lett. 109, 233601 (2012).

[10] R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, ``The elusive Heisenberg limit in quantum-enhanced metrology,'' Nat. Commun. 3, 1063 (2012).

[11] A. Chenu, M. Beau, J. Cao, and A. del Campo, ``Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise,'' Phys. Rev. Lett. 118, 140403 (2017).

[12] D. M. Reich, M. Ndong, and C. P. Koch, ``Monotonically convergent optimization in quantum control using Krotov's method,'' J. Chem. Phys. 136, 104103 (2012).

[13] T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, and G. E. Santoro, ``Optimal control at the quantum speed limit,'' Phys. Rev. Lett. 103, 240501 (2009).

[14] A. del Campo, M. M. Rams, and W. H. Zurek, ``Assisted Finite-Rate Adiabatic Passage Across a Quantum Critical Point: Exact Solution for the Quantum Ising Model,'' Phys. Rev. Lett. 109, 115703 (2012).

[15] G. C. Hegerfeldt, ``Driving at the Quantum Speed Limit: Optimal Control of a Two-Level System,'' Phys. Rev. Lett. 111, 260501 (2013).

[16] M. Murphy, S. Montangero, V. Giovannetti, and T. Calarco, ``Communication at the quantum speed limit along a spin chain,'' Phys. Rev. A 82, 022318 (2010).

[17] S. An, D. Lv, A. del Campo, and K. Kim, ``Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space,'' Nat. Commun. 7, 12999 (2016).

[18] S. Campbell and S. Deffner, ``Trade-Off Between Speed and Cost in Shortcuts to Adiabaticity,'' Phys. Rev. Lett. 118, 100601 (2017).

[19] K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, ``Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving,'' Phys. Rev. Lett. 118, 100602 (2017).

[20] F. Campaioli, F. A. Pollock, F. C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, and K. Modi, ``Enhancing the Charging Power of Quantum Batteries,'' Phys. Rev. Lett. 118, 150601 (2017a).

[21] F. Campaioli, F. A. Pollock, and S. Vinjanampathy, ``Quantum batteries,'' in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International Publishing, Cham, 2018) pp. 207–225.

[22] M. Okuyama and M. Ohzeki, ``Quantum Speed Limit is Not Quantum,'' Phys. Rev. Lett. 120, 070402 (2018).

[23] B. Shanahan, A. Chenu, N. Margolus, and A. del Campo, ``Quantum Speed Limits across the Quantum-to-Classical Transition,'' Phys. Rev. Lett. 120, 070401 (2018).

[24] J. Kupferman and B. Reznik, ``Entanglement and the speed of evolution in mixed states,'' Phys. Rev. A 78, 042305 (2008).

[25] R. Uzdin, U. Günther, S. Rahav, and N. Moiseyev, ``Time-dependent Hamiltonians with 100% evolution speed efficiency,'' J. Phys. A Math. Theor. 45, 415304 (2012).

[26] A. C. Santos and M. S. Sarandy, ``Superadiabatic Controlled Evolutions and Universal Quantum Computation,'' Sci. Rep. 5, 15775 (2015).

[27] A. C. Santos, R. D. Silva, and M. S. Sarandy, ``Shortcut to adiabatic gate teleportation,'' Phys. Rev. A 93, 012311 (2016).

[28] J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, ``The role of quantum information in thermodynamics—a topical review,'' J. Phys. A Math. Theor. 49, 143001 (2016).

[29] R. Uzdin and R. Kosloff, ``Speed limits in Liouville space for open quantum systems,'' EPL (Europhysics Lett. 115, 40003 (2016).

[30] D. Mondal, C. Datta, and S. Sazim, ``Quantum coherence sets the quantum speed limit for mixed states,'' Phys. Lett. A 380, 689 (2015).

[31] D. Mondal and A. K. Pati, ``Quantum speed limit for mixed states using an experimentally realizable metric,'' Phys. Lett. A 380, 1395 (2016).

[32] N. Mirkin, F. Toscano, and D. A. Wisniacki, ``Quantum-speed-limit bounds in an open quantum evolution,'' Phys. Rev. A 94, 052125 (2016).

[33] D. P. Pires, M. Cianciaruso, L. C. Céleri, G. Adesso, and D. O. Soares-Pinto, ``Generalized Geometric Quantum Speed Limits,'' Phys. Rev. X 6, 021031 (2016).

[34] I. Marvian, R. W. Spekkens, and P. Zanardi, ``Quantum speed limits, coherence, and asymmetry,'' Phys. Rev. A 93, 052331 (2016).

[35] N. Friis, M. Huber, and M. Perarnau-Llobet, ``Energetics of correlations in interacting systems,'' Phys. Rev. E 93, 042135 (2016).

[36] J. M. Epstein and K. B. Whaley, ``Quantum speed limits for quantum-information-processing tasks,'' Phys. Rev. A 95, 042314 (2017).

[37] A. Ektesabi, N. Behzadi, and E. Faizi, ``Improved bound for quantum-speed-limit time in open quantum systems by introducing an alternative fidelity,'' Phys. Rev. A 95, 022115 (2017).

[38] B. Russell and S. Stepney, ``The Geometry of Speed Limiting Resources in Physical Models of Computation,'' Int. J. Found. Comput. Sci. 28, 321 (2017).

[39] L. P. García-Pintos and A. del Campo, ``Quantum speed limits under continuous quantum measurements,'' New Journal of Physics 21, 033012 (2019).

[40] K. Berrada, ``Quantum speedup in structured environments,'' Phys. E Low-dimensional Syst. Nanostructures 95, 6 (2018).

[41] A. C. Santos and M. S. Sarandy, ``Generalized shortcuts to adiabaticity and enhanced robustness against decoherence,'' J. Phys. A Math. Theor. 51, 025301 (2018).

[42] C.-K. Hu, J.-M. Cui, A. C. Santos, Y.-F. Huang, M. S. Sarandy, C.-F. Li, and G.-C. Guo, ``Experimental implementation of generalized transitionless quantum driving,'' Opt. Lett. 43, 3136 (2018).

[43] T. Volkoff and K. Whaley, ``Distinguishability times and asymmetry monotone-based quantum speed limits in the Bloch ball,'' Quantum 2, 96 (2018).

[44] G. Fubini, ``Sulle metriche definite da una forma Hermitiana,'' Atti Istit. Veneto 63, 502 (1904).

[45] E. Study, ``Kürzeste Wege im komplexen Gebiet,'' Math. Ann. 60, 321 (1905).

[46] I. Bengtsson and K. Zyczkowski, Geometry of quantum states : an introduction to quantum entanglement (Cambridge University Press, 2008) p. 419.

[47] L. B. Levitin and T. Toffoli, ``Fundamental limit on the rate of quantum dynamics: The unified bound is tight,'' Phys. Rev. Lett. 103, 160502 (2009).

[48] S. Deffner and E. Lutz, ``Quantum Speed Limit for Non-Markovian Dynamics,'' Phys. Rev. Lett 111, 010402 (2013b).

[49] A. del Campo, I. L. Egusquiza, M. B. Plenio, and S. F. Huelga, ``Quantum Speed Limits in Open System Dynamics,'' Phys. Rev. Lett. 110, 050403 (2013).

[50] Z. Sun, J. Liu, J. Ma, and X. Wang, ``Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation,'' Sci. Rep. 5, 8444 (2015).

[51] F. Campaioli, F. A. Pollock, F. C. Binder, and K. Modi, ``Tightening Quantum Speed Limits for Almost All States,'' Phys. Rev. Lett. 120, 060409 (2017b).

[52] M. Keyl and R. F. Werner, ``Estimating the spectrum of a density operator,'' Phys. Rev. A 64, 052311 (2001).

[53] A. K. Ekert, C. M. Alves, D. K. L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, ``Direct Estimations of Linear and Nonlinear Functionals of a Quantum State,'' Phys. Rev. Lett. 88, 217901 (2002).

[54] B. Russell and S. Stepney, ``Applications of Finsler Geometry to Speed Limits to Quantum Information Processing,'' Int. J. Found. Comput. Sci. 25, 489 (2014).

[55] W. K. Wootters, ``Statistical distance and Hilbert space,'' Phys. Rev. D 23, 357 (1981).

[56] M. S. Byrd and N. Khaneja, ``Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation,'' Phys. Rev. A 68, 062322 (2003).

[57] M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. De Matos Filho, ``Quantum speed limit for physical processes,'' Phys. Rev. Lett. 110, 050402 (2013).

[58] D. Pérez-García, M. M. Wolf, D. Petz, and M. B. Ruskai, ``Contractivity of positive and trace-preserving maps under Lp norms,'' J. Math. Phys. 47, 083506 (2006).

[59] M. Piani, ``Problem with geometric discord,'' Phys. Rev. A 86, 034101 (2012).

[60] E. Il'ichev, N. Oukhanski, A. Izmalkov, T. Wagner, M. Grajcar, H.-G. Meyer, A. Y. Smirnov, A. Maassen van den Brink, M. H. S. Amin, and A. M. Zagoskin, ``Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit,'' Phys. Rev. Lett. 91, 097906 (2003).

[61] D. Zueco, G. M. Reuther, S. Kohler, and P. Hänggi, ``Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation,'' Phys. Rev. A 80, 033846 (2009).

[62] C. A. Rodríguez-Rosario, G. Kimura, H. Imai, and A. Aspuru-Guzik, ``Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment,'' Phys. Rev. Lett. 106, 050403 (2011).

[63] H.-P. Breuer and F. F. Petruccione, The theory of open quantum systems (Oxford University Press, 2002) p. 625.

[64] F. A. Pollock and K. Modi, ``Tomographically reconstructed master equations for any open quantum dynamics,'' Quantum 2, 76 (2017).

[65] A. Uhlmann, ``An energy dispersion estimate,'' Phys. Lett. A 161, 329 (1992).

[66] S. Luo and Q. Zhang, ``Informational distance on quantum-state space,'' Phys. Rev. A 69, 032106 (2004).

[67] P. Facchi, R. Kulkarni, V. Man'ko, G. Marmo, E. Sudarshan, and F. Ventriglia, ``Classical and quantum Fisher information in the geometrical formulation of quantum mechanics,'' Phys. Lett. A 374, 4801 (2010).

[68] J. A. Miszczak, Z. Puchała, P. Horodecki, A. Uhlmann, and K. Życzkowski, ``Sub– and super–fidelity as bounds for quantum fidelity,'' Quantum Inf. Comput. 9 (2009), arXiv:0805.2037.

[69] J. Abernethy, F. Bach, and T. Evgeniou, ``A new approach to collaborative filtering: Operator estimation with spectral regularization,'' J. Mach. Learn. Res. 10, 803 (2009).

[70] X. Wang, M. Allegra, K. Jacobs, S. Lloyd, C. Lupo, and M. Mohseni, ``Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems,'' Phys. Rev. Lett. 114, 170501 (2015).

[71] J. Geng, Y. Wu, X. Wang, K. Xu, F. Shi, Y. Xie, X. Rong, and J. Du, ``Experimental Time-Optimal Universal Control of Spin Qubits in Solids,'' Phys. Rev. Lett. 117, 170501 (2016).

[72] C. Arenz, G. Gualdi, and D. Burgarth, ``Control of open quantum systems: case study of the central spin model,'' New Journal of Physics 16, 065023 (2014).

[73] J. Lee, C. Arenz, H. Rabitz, and B. Russell, ``Dependence of the quantum speed limit on system size and control complexity,'' New Journal of Physics 20, 063002 (2018).

[74] C. Arenz, B. Russell, D. Burgarth, and H. Rabitz, ``The roles of drift and control field constraints upon quantum control speed limits,'' New Journal of Physics 19, 103015 (2017).

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[2] Niaz Ali Khan, Munsif Jan, Muzamil Shah, and Darvaish Khan, "Quantum speed limit time in a relativistic frame", Annals of Physics 440, 168831 (2022).

[3] J Teittinen, H Lyyra, and S Maniscalco, "There is no general connection between the quantum speed limit and non-Markovianity", New Journal of Physics 21 12, 123041 (2019).

[4] Tian-Niu Xu, Jing Li, Thomas Busch, Xi Chen, and Thomás Fogarty, "Effects of coherence on quantum speed limits and shortcuts to adiabaticity in many-particle systems", Physical Review Research 2 2, 023125 (2020).

[5] Eoin O'Connor, Giacomo Guarnieri, and Steve Campbell, "Action quantum speed limits", Physical Review A 103 2, 022210 (2021).

[6] Katarzyna Bolonek-Lasoń, Joanna Gonera, and Piotr Kosiński, "Classical and quantum speed limits", Quantum 5, 482 (2021).

[7] Lu Hou, Bin Shao, and Chaoquan Wang, "Quantum Speed Limit Under the Influence of Measurement-based Feedback Control", International Journal of Theoretical Physics 62 2, 47 (2023).

[8] N. Awasthi, S. Haseli, U. C. Johri, S. Salimi, H. Dolatkhah, and A. S. Khorashad, "Quantum speed limit time for correlated quantum channel", Quantum Information Processing 19 1, 10 (2020).

[9] Yanyan Shao, Bo Liu, Mao Zhang, Haidong Yuan, and Jing Liu, "Operational definition of a quantum speed limit", Physical Review Research 2 2, 023299 (2020).

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[11] Paulina Marian and Tudor A. Marian, "Quantum speed of evolution in a Markovian bosonic environment", Physical Review A 103 2, 022221 (2021).

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[13] Maxwell Aifer and Sebastian Deffner, "From quantum speed limits to energy-efficient quantum gates", New Journal of Physics 24 5, 055002 (2022).

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[18] Wei Wu and Jun-Hong An, "Quantum speed limit of a noisy continuous-variable system", Physical Review A 106 6, 062438 (2022).

[19] D. Z. Rossatto, D. P. Pires, F. M. de Paula, and O. P. de Sá Neto, "Quantum coherence and speed limit in the mean-field Dicke model of superradiance", Physical Review A 102 5, 053716 (2020).

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[22] Yi-Zheng Zhen, Dario Egloff, Kavan Modi, and Oscar Dahlsten, "Universal Bound on Energy Cost of Bit Reset in Finite Time", Physical Review Letters 127 19, 190602 (2021).

[23] Soroush Haseli, "The Effect of Homodyne-Based Feedback Control on Quantum Speed Limit Time", International Journal of Theoretical Physics 59 6, 1927 (2020).

[24] Francesco Campaioli, Chang-shui Yu, Felix A Pollock, and Kavan Modi, "Resource speed limits: maximal rate of resource variation", New Journal of Physics 24 6, 065001 (2022).

[25] Adolfo del Campo, "Probing Quantum Speed Limits with Ultracold Gases", Physical Review Letters 126 18, 180603 (2021).

[26] Kohei Kobayashi and Naoki Yamamoto, "Quantum speed limit for robust state characterization and engineering", Physical Review A 102 4, 042606 (2020).

[27] Xiang Lu, Ying-Jie Zhang, and Yun-Jie Xia, "Coherent-driving-assisted quantum speedup in Markovian channels* ", Chinese Physics B 30 2, 020301 (2021).

[28] Xu Kai, Han-Jie Zhu, Guo-Feng Zhang, Jie-Ci Wang, and Wu-Ming Liu, "Quantum speedup dynamics process in Schwarzschild space–time", Results in Physics 35, 105278 (2022).

[29] 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).

[30] Niklas Hörnedal, Nicoletta Carabba, Apollonas S. Matsoukas-Roubeas, and Adolfo del Campo, "Ultimate speed limits to the growth of operator complexity", Communications Physics 5 1, 207 (2022).

[31] Jérôme Denis and John Martin, "Extreme depolarization for any spin", Physical Review Research 4 1, 013178 (2022).

[32] Klaus Liegener and Łukasz Rudnicki, "Quantum speed limit and stability of coherent states in quantum gravity", Classical and Quantum Gravity 39 12, 12LT01 (2022).

[33] A. A. Dìaz V., V. Martikyan, S. J. Glaser, and D. Sugny, "Purity speed limit of open quantum systems from magic subspaces", Physical Review A 102 3, 033104 (2020).

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[39] Dorje C. Brody and Bradley Longstaff, "Evolution speed of open quantum dynamics", Physical Review Research 1 3, 033127 (2019).

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

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