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Quantum cloning and the capacity of the Pauli channel

Nicolas J. Cerf
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Abstract

A family of quantum cloning machines is introduced that produce two approximate copies from a single quantum bit, while the overall input-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, describing the balance between the quality of the two copies. This also provides an upper bound on the quantum capacity of the Pauli channel with probabilities $p_x$, $p_y$ and $p_z$. The capacity is shown to be vanishing if $(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies outside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine.

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Nicolas J. Cerf. 1998-03-30. Quantum cloning and the capacity of the Pauli channel. https://doi.org/10.1103/physrevlett.84.4497

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