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Annalen der Physik

Universal Global Cloning of Continuous Variables Entanglement

Li Ge, Jun Xin, Lin Zhang

Published Dec 14, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1002/andp.202200453

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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.
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.
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
Quantum theory fundamentally forbids the perfect copying of an arbitrary unknown quantum state, according to a principle known as the no-cloning theorem. Nevertheless, it is possible to construct a deterministic quantum map that produces multiple approximate copies of an unknown quantum state. This task is referred to as universal quantum cloning, further facilitating numerous quantum technologies such as quantum cryptography and quantum communication. In this work, we theoretically verify that the universal quantum cloning cannot be realized within a noncontextual theory, highlighting its intrinsically nonclassical nature. Our verification first {focuses on revealing that} 1→21\rightarrow21→2 cloning scenario {is fully contextual}, and {further covers general examples to observe the contextual behavior of} N→MN\rightarrow MN→M scenario. We believe that our results regarding quantum cloning serve a key role for understanding both quantum foundation and application.
We study the problem of universal quantum cloning – taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.
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.
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.