Sergii Strelchuk, Michał Horodecki, Jonathan Oppenheim
The first teleportation protocol that does not require correction after the measurement is port-based teleportation introduced by Hiroshima and Ishizaka. It uses a large resource state consisting of N singlets to teleport only a single qubit state reliably. We provide two distinct protocols which recycle the resource state to teleport f(\epsilon) N states with error \epsilon, where f(\epsilon) is a linear function of \epsilon. The first protocol consists of sequentially teleporting qubit states, and the second one teleports them in a bulk. Next, we discuss possible generalizations of existing teleportation protocols. Thus far, all known protocols can be viewed as teleportation over the Pauli group or the symmetric permutation group. We derive sufficient condition for a set of operations, which in general need not form a group to be used in port-based teleportation protocols, potentially leading to new teleportation protocols with novel properties.
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http://arxiv.org/abs/1209.2683
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