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

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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Cited by

[1] Daniel Basilewitsch, Christiane P. Koch, and Daniel M. Reich, "Quantum Optimal Control for Mixed State Squeezing in Cavity Optomechanics", arXiv:1807.04718.

[2] Junjie Liu, Dvira Segal, and Gabriel Hanna, "Hybrid quantum-classical simulation of quantum speed limits in open quantum systems", Journal of Physics A Mathematical General 52 21, 215301 (2019).

[3] Ken Funo, Naoto Shiraishi, and Keiji Saito, "Speed limit for open quantum systems", New Journal of Physics 21 1, 013006 (2019).

[4] Francesco Campaioli, William Sloan, Kavan Modi, and Felix Alexander Pollock, "An algorithm for solving unconstrained unitary quantum brachistochrone problems", arXiv:1906.02934.

[5] Dorje C Brody and Bradley Longstaff, "Evolution speed of open quantum dynamics", arXiv:1906.04766.

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