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 Sn (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 details 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.

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