Quantum cloning and the capacity of the Pauli channel

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.

5 pages RevTeX, 3 Postscript figures

References in corpus (4)

• Optimal Quantum Cloning Machines
• Optimal Universal and State-Dependent Quantum Cloning
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• Optimal Copying of One Quantum Bit

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