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Optica Publishing Group
  • 2013 Conference on Lasers and Electro-Optics - International Quantum Electronics Conference
  • (Optica Publishing Group, 2013),
  • paper IB_P_5

Entanglement Swapping with Local Certification: Application to Remote Micromechanical Resonators

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Abstract

Entanglement swapping allows to entangle two distant systems which never interacted. The standard protocol considers two distant users, Alice and Bob, each possessing a bipartite entangled system, R1B1 for Alice and R2B2 for Bob. The users send their systems B1 and B2 to an intermediate station (Charlie). Here an appropriate Bell measurement is made over the B systems and the outcome communicated back to Alice and Bob. As a result, the two remote systems R1 and R2 become entangled. A delicate point is the experimental verification of the generated entanglement, which generally involves direct measurements on the two remote systems, R1 and R2, followed by classical communications. A simple local alternative approach for verifying the success of swapping is based on the local certification protocol proposed here. The key idea is to extend the initial systems of Alice and Bob from bipartite to tripartite. We add a certification system (C) to each site, so that we have tripartite system R1B1C1 for Alice and another R2B2C2 for Bob. In this new protocol, also the certification systems C1 and C2 are sent to Charlie’s station, where they are locally measured. This additional measurement enables Charlie to certify the generation of entanglement for the two remote systems R1 and R2. However, one cannot use arbitrary tripartite states but a suitable class of states must be engineered, that we call “certifying”. In the case of Gaussian continuous variable state the certifying condition involves local and bipartite purities and it is given by µRB > µBC > µB. This condition implies the following inequalities for the bipartite logarithmic negativities, ENR1R2>ENC1C2>0. This means that performing the entanglement swapping protocol with a certifying state allows to entangle both the C1C2 and the R1R2 bipartite subsystems, with the latter one more entangled than the former one. Therefore the detection by Charlie of entanglement in the certification subsystem C1C2 guarantees the generation of remote entanglement, i.e., between the remote modes, R1 and R2, in Alice’s and Bob’s stations.

© 2013 IEEE

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