Critical assessment of information back-flow in measurement-free teleportation

We assess a scheme for measurement-free quantum teleportation from the perspective of the resources underpinning its performance. In particular, we focus on claims recently made 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 the efficiency of teleportation and the 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.