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

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.

13 pages, 3 figures, final version to appear in Physics Letters A

References in corpus (4)

• Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
• Unified Universal Quantum Cloning Machine and Fidelities
• A stronger no-cloning theorem
• Generalised Asymmetric Quantum Cloning

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• Explicit constructions of unitary transformations between equivalent irreducible representations
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry
• A geometrical description of the universal $1\to 2$ asymmetric quantum cloning region
• The Asymmetric Quantum Cloning Region