Generation of field-mediated three-qubit entangled state shared by Alice and Bob

Abstract

A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits ${A}_{1}$ and ${A}_{2}$) entangled to a single-trapped atom in a remote laboratory owned by Bob $(B)$, is proposed. The entanglement is generated through interaction of trapped atoms with two-mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of Son et al. [J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativity detects the free entanglement of the three atom mixed state, the bound entanglement is detected by the negativity calculated from pure state decomposition of the state operator. The partial negativities calculated by selective partial transposition of the three atom mixed state detect the pairwise entanglement of qubit pairs ${A}_{1}B$, ${A}_{2}B$, and ${A}_{1}{A}_{2}$. The entanglement of three atoms is found to be $W$-like, no Greenberger-Horne-Zeilinger-like quantum correlations being generated.