Quantum repeaters based on trapped ions with decoherence free subspace encoding. (arXiv:1611.07779v2 [quant-ph] UPDATED)

Quantum repeaters provide an efficient solution to distribute Bell pairs over
arbitrarily long distances. While scalable architectures are demanding
regarding the number of qubits that need to be controlled, here we present a
quantum repeater scheme aiming to extend the range of present day quantum
communications that could be implemented in the near future with trapped ions
in cavities. We focus on an architecture where ion-photon entangled states are
created locally and subsequently processed with linear optics to create
elementary links of ion-ion entangled states. These links are then used to
distribute entangled pairs over long distances using successive entanglement
swapping operations performed deterministically using ion-ion gates. We show
how this architecture can be implemented while encoding the qubits in a
decoherence free subspace to protect them against collective dephasing. This
results in a protocol that can be used to violate a Bell inequality over
distances of about 800 km assuming state of the art parameters. We discuss how
this could be improved to several thousand kilometers in future setups.

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