Discrimination between evolution operators

TL;DR

This paper demonstrates that, under broad conditions, evolutions caused by different Hamiltonians can produce orthogonal states, simplifying experimental discrimination between quantum evolutions compared to previous methods.

Contribution

It shows that orthogonal states can be generated by different Hamiltonians under broad conditions and provides a simpler experimental approach for their discrimination.

Findings

Orthogonal states can be achieved for most Hamiltonian pairs.

Discrimination is experimentally simpler than previous methods.

A lower bound for orthogonalization time is proposed.

Abstract

Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is demonstrated for every scenario but a special one. This discrimination between evolutions is experimentally much simpler than procedures proposed earlier based on either sequential or parallel application of the unknown unitaries. A lower bound for the orthogonalization time is proposed in terms of the properties of the two Hamiltonians.