Universal quantum cloning

Vladimír Bužek, Mark S. Hillery

We analyze how information encoded in quantum systems can be optimally processed. In particular, we investigate copying (cloning) of quantum information (represented as states of 2-level quantum systems--qubits). We present unitary transformations which describe the optimal universal cloning of a qubit. Universality of the transformation guarantees that the fidelity of the cloning does not depend on the input state of the qubit, i.e. all states are cloned equally well. We present network for the optimal universal quantum cloning `machine' (transformation) which produces N + 1 copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copes, N. We also present the `machine' which universally and optimally clones states of quantum objects in arbitrary- dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers. In addition to cloning of qubits we analyzed another universal operation-- the Universal NOT. We present the optimal transformation and the corresponding logical network which optimally complements an arbitrary input state of a qubit. We show that the fidelity of the performance of the Universal NOT operation increases as a function of the number of input qubits prepared in the same state.

Zhen‐Biao Yang, Pei-Rong Han, Xin-Jie Huang +6 more

Abstract No-cloning theorem forbids perfect cloning of an unknown quantum state. A universal quantum cloning machine (UQCM), capable of producing two copies of any input qubit with the optimal fidelity, is of fundamental interest and has applications in quantum information processing. This is enabled by delicately tailored nonclassical correlations between the input qubit and the copying qubits, which distinguish the UQCM from a classical counterpart, but whose experimental demonstrations are still lacking. We here implement the UQCM in a superconducting circuit and investigate these correlations. The measured entanglements well agree with our theoretical prediction that they are independent of the input state and thus constitute a universal quantum behavior of the UQCM that was not previously revealed. Another feature of our experiment is the realization of deterministic and individual cloning, in contrast to previously demonstrated UQCMs, which either were probabilistic or did not constitute true cloning of individual qubits.

Miguel Orszag

Li Ge, Jun Xin, Lin Zhang

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.

Miguel Orszag