Entanglement Recycling in Two-Step Port-Based Teleportation

A protocol involving the repetitive (twofold, to be precise) application of PBT protocol to the same resource is studied. The quantities characterizing the resulting protocol, so-called two-step PBT, namely enatnglement fidelity and success probability are provided for two scenarios, relying on application of pretty-good measurement, i.e. deterministic and probabilistic PBT with non-EPR resource. This results show that two-step PBT is an accurate protocol, provided the resource is sufficiently large. In particular, the deterministic two-step PBT obtains fidelity that is remarkably close to the optimal MPBT fidelity for teleportation of two quantum states. Additionally, the recycling fidelity, i.e. the quantity characterizing the degradation of the resource state is calculated for repetitive application of probabilistic protocol, for both EPR and optimized resource, showing that entanglement recycling with two-step PBT is possible in the former case as well.