The correspondence principle suggests that a quantum description for the microworld should be naturally transited to a classical description within the classical limit. However, it seems that there is a large gap between quantum no-cloning and classical duplication. In this paper, we prove that a classical duplication process can be realized using a universal quantum cloning machine. In the classical world, information is encoded in a large number of quantum states instead of one quantum state. When tolerable errors occur in a small number of the quantum states, the fidelity of duplicated copies of classical information can approach unity. That is, classical information duplication is equivalent to a redundant quantum cloning process with self-correcting.
The correspondence principle suggests that a quantum description for the microworld should be naturally transited to a classical description within the classical limit. However, it seems that there is a large gap between quantum no-cloning and classical duplication. In this paper, we prove that a classical duplication process can be realized using a universal quantum cloning machine. In the classical world, information is encoded in a large number of quantum states instead of one quantum state. When tolerable errors occur in a small number of the quantum states, the fidelity of duplicated copies of classical information can approach unity. That is, classical information duplication is equivalent to a redundant quantum cloning process with self-correcting.
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.
Quantum internet, which is expected to be a combination of quantum and classical networks, promises to provide information-theoretic security for data exchange. Classical networks have well-established protocols for reliable end-to-end transmission that implicitly make use of duplicating classical bits. However, quantum bits (qubits) cannot be copied due to the no-cloning theorem. In this paper, we take advantage of the principle of creating imperfect clones using a Universal Quantum Copying Machine (UQCM) and propose the Quantum Automatic Repeat Request (QARQ) protocol, inspired by its classical equivalent. A simulation platform has been developed to study the feasibility of QARQ. Results show that our proposal is well suited for applications that are compatible with low fidelity requirements.
No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.
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.
Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O(M/N 2), where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i) an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii) a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N 2, and iii) a protocol that generates O(N 2) nearly perfect copies of a generic pure state U |0〉 while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M 2/N 2.
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.