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Port-based teleportation (PBT) is a protocol of quantum teleportation inwhich a receiver does not have to apply correction to the transmitted state. Inthis protocol two spatially separated parties can teleport an unknown quantumstate only by exploiting joint measurements on number of shared $d-$dimensionalmaximally entangled states (resource state) together with a state to beteleported and one way classical communication. In this paper we analyse forthe first time the recycling protocol for the deterministic PBT beyond thequbit case. In the recycling protocol the main idea is to re-use the remainingresource state after one or many rounds of PBT for further processes ofteleportation. The key property is to learn how much the underlying resourcestate degrades after every round of the teleportation process. We measure thisby evaluating quantum fidelity between respective resource states. To do so wefirst present analysis of the square-root measurements used by the sender inPBT by exploiting the symmetries of the system. In particular, we show how toeffectively evaluate their square-roots and composition. These findings allowus to present the explicit formula for the recycling fidelity involving onlygroup-theoretic parameters describing irreducible representations in theSchur-Weyl duality. For the first time, we also analyse the degradation of theresource state for the optimal PBT scheme and show its degradation for all$d\geq 2$. In the both versions, the qubit case is discussed separatelyresulting in compact expression for fidelity, depending only on the number ofshared entangled pairs.

Square-root measurements and degradation of the resource state in port-based teleportation scheme