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arXiv:quant-ph/0302173 · Physical Review A

Cloning the entanglement of a pair of quantum bits

L.-P. Lamoureux, Patrick Navez, Jaromı́r Fiurášek, Nicolas J. Cerf

Published Apr 5, 2004• 29 citations
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Abstract

It is shown that any quantum operation that perfectly clones the entanglement of all maximally entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.

DOI
10.1103/physreva.69.040301

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It is shown that any quantum operation that perfectly clones the entanglement of all maximally entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of ddd-dimensional quantum systems prepared in an arbitrary isotropic state. It maximizes the entanglement of formation contained in the two copies of any maximally entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of isotropic states. For large ddd, the entanglement of formation of each clone tends to one-half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one-fourth the input entanglement in the large-ddd limit.
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Abstract It is impossible to perfectly duplicate an unknown entangled state while preserving inseparability, which is known as the entanglement no‐cloning principle. Nevertheless, approximate cloning of entanglement is allowed by quantum mechanics. A universal entanglement cloning machine (UECM) duplicates an entangled state such that the quality of its entanglement replicas does not depend on the input. To duplicate entanglement shared between two parties, 1‐to‐N universal local entanglement cloning machine (ULECM) has already been proposed (Weedbrook, et al., Phys. Rev. A, 77, 052313 (2008)), which employs two local UECMs to copy each party of the entangled state. However, the ULECM can never preserve the inseparability in its replicas. Here, a 1‐to‐N universal global entanglement cloning machine (UGECM) that takes the entire entangled state as the input and then globally clone it to produce replicas is proposed. It is demonstrated that the UGECM outperforms the ULECM both in terms of the fidelity and the inseparability preservation. In addition, the UGECM is of more simple and easy structure, compared with the UGECM. Such a UGECM may find its new applications in quantum entanglement broadcasting.