On Hamiltonians Generating Optimal-Speed Evolutions

Details On Hamiltonians Generating Optimal-Speed Evolutions On Hamiltonians Generating Optimal-Speed Evolutions

2008-04-30

arxiv.org/abs/0804.4755v4

Phys. Rev. A 79, 014101 (2009)

Physics

Quantum Physics

Published version

Scientific paper

10.1103/PhysRevA.79.014101

We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric- (inner product-) dependence of the lower bound on the travel time and the universality (metric-independence) of the upper bound on the speed of unitary evolutions.

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