Process-optimized phase covariant quantum cloning

TL;DR

This paper computes the optimal global fidelity for phase-covariant quantum cloning machines using semi-definite programming, advancing the understanding of their performance and simulation methods.

Contribution

It provides the first calculation of optimal global fidelity for phase-covariant QCMs and analyzes simulation strategies for cloning and transpose cloning maps.

Findings

Optimal global fidelity computed for phase-covariant QCMs.

Composition method is sub-optimal for cloning map.

Composition method is asymptotically optimal for transpose cloning.

Abstract

After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM, single-qudit fidelity and global fidelity have been most widely used. In this paper we compute the optimal global fidelity for phase-covariant cloning machines via semi-definite programming optimization, thereby completing a remaining gap in the previous results on QCMs. We also consider optimal simulations of the cloning and transpose cloning map, both by a direct optimization and by a composition of component-wise optimal QCMs. For the cloning map the composition method is sub-optimal whereas for the transpose cloning map the method is asymptotically optimal.