Piotr Ćwikliński, Michał Horodecki, Michał Studziński
We analyze the region of fidelities for qubits which is obtained after
performing quantum cloning, by means of 1-3 universal quantum cloner. To obtain
our result, we apply to our problem group representation theory, namely Schur -
Weyl decomposition. We express the allowed region for fidelities in terms of
overlaps of pure states with irreps of $S_n$. We then show that the pure states
can be taken with real coefficients. Subsequently, the case $n=4$,
corresponding to 1-3 cloner is studied in more detail. We first obtain a plot
of possible range of fidelities for qubits related to a given irrep
(irreducible representation) and then make a convex hull of it to obtain the
allowed region of triples of fidelities. The method allows to construct the
state giving rise to a given triple of fidelities.
View original:
http://arxiv.org/abs/1201.6077
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