Abstract
We assess a scheme for measurement-free quantum teleportation from the perspective of the resources underpinning its performance. In particular, we focus on recently made claims about the crucial role played by the degree of non-Markovianity of the dynamics of the information carrier whose state we aim to teleport. We prove that any link between efficiency of teleportation and back-flow of information depends fundamentally on the way the various operations entailed by the measurement-free teleportation protocol are implemented, while - in general - no claim of causal link can be made. Our result reinforces the need for the explicit assessment of the underlying physical platform when assessing the performance and resources for a given quantum protocol and the need for a rigorous quantum resource theory of non-Markovianity.
