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arXiv:quant-ph/0502103 · Physical Review A

Usefulness of classical communication for local cloning of entangled states

Rafał Demkowicz-Dobrzański, Maciej Lewenstein, Aditi Sen, Ujjwal Sen, Dagmar Bruß

Published Mar 15, 2006• 9 citations
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Abstract

We solve the problem of the optimal cloning of pure entangled two-qubit states with a fixed degree of entanglement using local operations and classical communication. We show that, amazingly, classical communication between the parties can improve the fidelity of local cloning if and only if the initial entanglement is higher than a certain critical value. It is completely useless for weakly entangled states. We also show that bound entangled states with positive partial transpose are not useful as a resource to improve the best local cloning fidelity.

DOI
10.1103/physreva.73.032313

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We solve the problem of the optimal cloning of pure entangled two-qubit states with a fixed degree of entanglement using local operations and classical communication. We show that, amazingly, classical communication between the parties can improve the fidelity of local cloning if and only if the initial entanglement is higher than a certain critical value. It is completely useless for weakly entangled states. We also show that bound entangled states with positive partial transpose are not useful as a resource to improve the best local cloning fidelity.
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We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in a blank copy is obtained for various cases. Surprisingly, this amount is more than 1 ebit for certain sets of two nonmaximal but equally entangled states of two qubits. To clone any three Bell states, at least log2 3{\text{log}}_{2}\text{ }3log2​ 3 ebit is necessary.
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