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.
Kruszynska and Kraus [Phys. Rev. A 79, 052304 (2009)] have recently introduced the so-called locally maximally entangleable (LME) states of
n qubits which can be maximally entangled with local auxiliary qubits using controlled operations. We characterize the local entangleability of hypergraph states and
W states using the approach of Kruszynska and Kraus. We show that (i) all hypergraph states are LME; (ii) hypergraph states and LME states are not equivalent under local unitaries; (iii) a
W state of
n qubits is not LME; and (iv) no hypergraph state of
n qubits can be converted into the
W state under local unitary transformations. Moreover, we also present an approach for encoding weighted hypergraphs into LME states.
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.