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arXiv · 2111.05677

Optimal bounds on the speed of subspace evolution

Sergio Albeverio·Alexander K. Motovilov
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Abstract

By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam-Tamm inequality that bounds the speed of the evolution of a state in terms of its energy dispersion. In contrast to the basic Mandelstam-Tamm inequality, we are concerned not with a single state but with a (possibly infinite-dimensional) subspace which is subject to the Schroedinger evolution. By using the concept of maximal angle between subspaces we derive optimal bounds on the speed of such a subspace evolution. These bounds may be viewed as further generalizations of the Mandelstam-Tamm inequality. Our study includes the case of unbounded Hamiltonians.

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Sergio Albeverio, Alexander K. Motovilov. 2021-11-10. Optimal bounds on the speed of subspace evolution. https://doi.org/10.1088/1751-8121%2Fac6bcf

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