Optimal asymmetric 1 → 4 quantum cloning in arbitrary dimension
We present an optimal asymmetric 1 → 4 quantum cloner. Our derivation generalizes the constructions of optimal asymmetric 1 → 2 and 1 → 3 quantum cloners in [Quantum Inf. Comput 5, 583 (2005)]. We explicitly prove the optimality of this cloner and give the maximum achievable fidelities. We also present the relation between the optimal quantum cloner with the multipartite entangled state which shows the singlet monogamy inequality in [Phys. Rev. Lett. 103, 050501 (2009)].
Arxiv – Unified Universal Quantum Cloning Machine and Fidelities (4 pages)
We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection which reduces dramatically the difficulties for implementation. Also it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities
No-cloning theorem is fundamental for quantum mechanics and quantum information science that states an unknown quantum state can not be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal quality, or instead, we can try to clone it perfectly with the largest probability. So various quantum cloning machines have been designed for different quantum information tasks. Experimentally, quantum cloning machines have been realized in optics system , nuclear magnetic resonance system, diamond nitrogen-vacancy center system, etc.
The universal quantum cloning machine is first proposed by Buzek and Hillery which can copy optimally one arbitrary qubit equally well to two copies. Later more general cases have been studied.
We present a unified optimal universal cloning machine. The cloning procession is equivalent with Werner cloning machine and the one proposed by Fan et al. and can be easily adjusted to asymmetric cloning machines and to the general case. This simple cloning machine is always realized by a symmetric projection and initially prepared maximally entangled states and thus should reduce the difficulties for implementation. Also the general fidelities are obtained. Our result offers a new platform for other cloning tasks for cases like phase-covariant and state-dependent.
Quantum cloning is the process that takes an arbitrary, unknown quantum state and makes an exact copy without altering the original state in any way. In Dirac notation.
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