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arXiv:quant-ph/0005070 · Chinese Physics Letters

Broadcasting of Entanglement in Three-Particle Greenberger-Horne-Zeilinger State via Quantum Copying

Zhao-Yang Tong, Kuang Le-Man

Published Jul 1, 2000• 8 citations
arXivHTMLPDF

Abstract

We introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in the three-particle Greenberger-Horne-Zeilinger (GHZ) state. The results show that the entanglement of the three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.

DOI
10.1088/0256-307x/17/7/001

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We introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in the three-particle Greenberger-Horne-Zeilinger (GHZ) state. The results show that the entanglement of the three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.
We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two WWW states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.
We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find that non-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state via non-local cloning exhibits the fidelity better than local cloning.
We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.
We study the degree to which quantum entanglement survives when a three-qubit entangled state iscopied by using local and non-local processes, respectively, and investigate iterating quantum copyingfor the three-qubitsystem. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system.We show that both local and non-local copying processes degrade quantum entanglement in the three-particle systemdue to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubitentanglement is preserved better than the inter-three-qubit entanglement in the local cloning process. We find thatnon-local cloning is much more efficient than the local copying for broadcasting entanglement, and output state vianon-local cloning exhibits the fidelity better than local cloning.
A protocol for probabilistic cloning of a class of three-qubit Greenberger-Horne-Zeilinger (GHZ) state and its orthogonal complement state by using three maximally two-qubit entangled states as the quantum channel is proposed.In this protocol,Bob(the state receiver) can receive the unknown state via usual teleportation process.With the assistance of Victor(the state preparer), Alice(the state sender) can produce the perfect copies and complement copies of an unknown state. A protocol for the teleportation is given by using non-maximally entangled states as quantum channel,and the clones and complement clones of unknown state also can be obtained by Alice with assistance offered by the state preparer.
We establish operational limits on the broadcasting of genuine multipartite entanglement (GME) in quantum networks. Using a distributed protocol in which each of N parties locally implements optimal 1 →\to→ 2 cloning via beam-splitter interactions, we derive exact expressions for the broadcast fidelity of Greenberger-Horne-Zeilinger (GHZ), W states, and Cluster states in a limited setting. We show that the fidelity decays exponentially with system size as [c(R)]N^NN, providing a quantitative expression of multipartite entanglement monogamy in the broadcasting setting, and that both state families share a universal normalisation factor arising from independent post-selection probabilities. Most significantly, we prove a no-go result for simultaneous GME certification: for all reflectivities and all system sizes, the two broadcast copies cannot be simultaneously certified as genuinely multipartite entangled within the standard framework of fidelity-based witnesses. We further check this behaviour for three- and four-party cluster states, finding consistent results that support the generality of the no-go beyond the GHZ and W families. This obstruction arises from the redistribution of multipartite coherence, which both reduces the achievable fidelity and increases the corresponding certification threshold. Our results reveal a fundamental trade-off between the broadcastability of multipartite entanglement and its operational certifiability, and delineate intrinsic limits on entanglement distribution in quantum networks.