Optimal bounds on the speed of subspace evolution
- URL: http://arxiv.org/abs/2111.05677v2
- Date: Thu, 26 May 2022 17:29:05 GMT
- Title: Optimal bounds on the speed of subspace evolution
- Authors: Sergio Albeverio, Alexander K. Motovilov
- Abstract summary: In contrast to the basic Mandelstam-Tamm inequality, we are concerned with a subspace 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.
- Score: 77.34726150561087
- License: http://creativecommons.org/licenses/by/4.0/
- 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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