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arXiv:2010.01888 · Physical Review Letters

Cloning of Quantum Entanglement

Li-Chao Peng, Dian Wu, Han-Sen Zhong, Yi-Han Luo, Yuan Li, Yi Hu, Xiao Qiang Jiang, Ming-Cheng Chen, Li Li, Nai-Le Liu, Kae Nemoto, William J. Munro, Barry C. Sanders, Chao‐Yang Lu, Jian-Wei Pan

Published Nov 17, 2020• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.210502

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Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.

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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.

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Bell Nonlocality: Guaranteeing Unclonable Quantum Teleportation

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Quantum teleportation, a cornerstone of quantum information science, allows for the transfer of an unknown quantum state without physically moving the associated quantum particle. This process critically relies on shared entanglement and classical communication. A fundamental aspect of quantum information is the no-cloning theorem, which dictates that an arbitrary unknown quantum state cannot be perfectly copied. This paper investigates the intrinsic connection between Bell nonlocality, a profound manifestation of quantum entanglement, and the inherent unclonability of quantum teleportation. We argue that the very existence of Bell nonlocality within the shared entangled resource not only enables quantum teleportation but also fundamentally guarantees that the teleported state cannot be perfectly cloned. By examining the theoretical underpinnings of Bell's theorem and the quantum teleportation protocol, we demonstrate how the non-local correlations preclude any possibility of state duplication, thereby upholding the no-cloning theorem. This connection is vital for understanding the security and foundational aspects of quantum communication, establishing Bell nonlocality as a strong certification of secure, non-duplicable quantum state transfer. The analysis highlights that successful quantum teleportation, intrinsically linked to the violation of Bell inequalities, provides an experimental signature of the non-classical correlations that underpin security against cloning.

•Nov 28, 2025•0 citations
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.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although such perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signalling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. Here, we perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states, and fully characterize our cloning machine by performing quantum state tomography on \emph{cloned} photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated in order to reveal the robustness of high-dimensional states in quantum cryptography.
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.
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.
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.
Quantum teleportation, a cornerstone of quantum information science, allows for the transfer of an unknown quantum state without physically moving the associated quantum particle. This process critically relies on shared entanglement and classical communication. A fundamental aspect of quantum information is the no-cloning theorem, which dictates that an arbitrary unknown quantum state cannot be perfectly copied. This paper investigates the intrinsic connection between Bell nonlocality, a profound manifestation of quantum entanglement, and the inherent unclonability of quantum teleportation. We argue that the very existence of Bell nonlocality within the shared entangled resource not only enables quantum teleportation but also fundamentally guarantees that the teleported state cannot be perfectly cloned. By examining the theoretical underpinnings of Bell's theorem and the quantum teleportation protocol, we demonstrate how the non-local correlations preclude any possibility of state duplication, thereby upholding the no-cloning theorem. This connection is vital for understanding the security and foundational aspects of quantum communication, establishing Bell nonlocality as a strong certification of secure, non-duplicable quantum state transfer. The analysis highlights that successful quantum teleportation, intrinsically linked to the violation of Bell inequalities, provides an experimental signature of the non-classical correlations that underpin security against cloning.