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

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

2012-01-29

arxiv.org/abs/1201.6077v2

Physics

Quantum Physics

13 pages, 3 figures

Scientific paper

We analyze a region of fidelities for qubit which is obtained after an application of a $1 \rightarrow N$ 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 $1 \rightarrow 3$ 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.

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