In this work, we revisit the problem of finding an admissible region of fidelities obtained after the application of an arbitrary $1\to N$ universal quantum cloner which has been recently solved in A. Kay et al. [Quant. Inf. Comput 13, 880 (2013)] from the side of cloning machines. Using group-theory formalism, we show that the allowed region for fidelities can be alternatively expressed in terms of overlaps of pure states with recently found irreducible representations of the commutant $U\otimes U\otimes \cdots \otimes U\otimes U^{*}$, which gives the characterization of the allowed region where states being cloned are a figure of merit. Additionally, it is sufficient to take pure states with real coefficients only, which makes calculations simpler. To obtain the allowed region, we make a convex hull of possible ranges of fidelities related to a given irrep. Subsequently, two cases, $1\to 2$ and $1\to 3$ cloners, are studied for different dimensions of states as illustrative examples.

• Received 24 February 2014

DOI:https://doi.org/10.1103/PhysRevA.89.052322