Quantum Operations: technical or fundamental challenge?

Bogdan Mielnik

Published 2013-05-16, updated 2013-12-02Version 3

A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as 'operation factories' transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract $\delta$-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, some other, to verify the existence of fundamental precision limits of the position measurements or the reality of `non-commutative geometries'.