Optimal bounds on the speed of subspace evolution

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.

arXiv comment15 pages

References in corpus (6)

• The maximum speed of dynamical evolution
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum speed limit for thermal states
• Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians
• Sharpening the norm bound in the subspace perturbation theory
• Quantum speed limits for time evolution of a system subspace

Cited by in corpus (1)

• Quantum speed limits for an open system in contact with a thermal bath