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 $\mathit{\text{two-step}}\mathit{\text{PBT}}$, namely $\mathit{\text{enatnglement}}\mathit{\text{fidelity}}$ and $\mathit{\text{success}}\mathit{\text{probability}}$ 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 $\mathit{\text{recycling}}\mathit{\text{fidelity}}$, 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.