Abstract
Port-based teleportation (PBT) is a quantum teleportation protocol, in which the parties exploit joint measurements performed on $N$ shared $d$-dimensional maximally entangled pairs (the resource) and the state to be teleported, with the addition of the one-way classical communication. The lack of correction in the last step is an essential feature distinguishing PBT from standard quantum teleportation. In my talk I shall consider the idea of entanglement recycling, i.e. the repeated use of the same resource for multiple rounds of PBT. The question is how the resource degrades after one or multiple uses. To answer it, we analyse the structure of the measurement employed in the protocol (the square-root-measurement, to be precise), depending greatly on the symmetries present in the system. In particular, as the result we evaluate its roots and compositions. These findings allow us to present the explicit formula for the recycling fidelity involving only group-theoretic parameters describing irreducible representations of the symmetric group $S(n)$. Additionally, I shall present the analysis of the resource degradation in the optimal PBT.
