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

TL;DR

This paper critically evaluates the role of non-Markovianity in measurement-free quantum teleportation, emphasizing that the efficiency depends on implementation details rather than a direct causal link with information back-flow.

Contribution

It demonstrates that the relationship between non-Markovianity and teleportation efficiency is not universal but depends on specific protocol implementations.

Findings

No inherent causal link between non-Markovianity and teleportation success.

Implementation details critically influence the role of information back-flow.

Highlights the importance of platform-specific assessment in quantum resource evaluation.

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.