Optimal processing of reversible quantum channels

Understand

We consider the general problem of the optimal transformation of N uses of (possibly different) unitary channels to a single use of another unitary channel in any finite dimension.

• We show how the optimal transformation can be fully parallelized, consisting in a preprocessing channel followed by a parallel action of all the N unitaries and a final postprocessing channel.
• Our techniques allow to achieve an exponential reduction in the number of the free parameters of the optimization problem making it amenable to an efficient numerical treatment.
• Finally, we apply our general results to find the analytical solution for special cases of interest like the cloning of qubit phase gates.