Optimal processing of reversible quantum channels

TL;DR

This paper develops a method for optimally transforming multiple uses of unitary channels into a single target channel, simplifying the optimization process and providing analytical solutions for specific cases like qubit phase gate cloning.

Contribution

It introduces a fully parallelized approach for optimal channel transformation that reduces computational complexity and offers analytical solutions for particular quantum channel cloning problems.

Findings

Optimal parallelization of channel transformation processes.

Exponential reduction in optimization parameters.

Analytical solutions for qubit phase gate cloning.

Abstract

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.