Region of fidelities for a 1 -> N universal qubit quantum cloner

TL;DR

This paper characterizes the range of achievable fidelities in a 1 -> N universal qubit quantum cloning process using group representation overlaps, providing a method to construct states with specified fidelities.

Contribution

It introduces a formalism based on irreducible representations to determine the fidelity region and construct states for universal qubit cloning.

Findings

Derived the fidelity region using overlaps of pure states with irreps.

Showed pure states can be taken with real coefficients only.

Analyzed the 1 -> 3 cloning case as an example.

Abstract

We analyze a region of fidelities for qubit which is obtained after an application of a 1 -> N universal quantum cloner. We express the allowed region for fidelities in terms of overlaps of pure states with irreps of S(n) (n = N+1) showing that the pure states can be taken with real coefficients only. Subsequently, the case n = 4, corresponding to a 1 -> 3 cloner is studied in more detail as an illustrative example. To obtain the main result, we make a convex hull of possible ranges of fidelities related to a given irrep. The formalism allows to construct the state giving rise to a given N-tuple of fidelities.