Certification of quantum networks using the generalised Choi isomorphism

We present a framework for certifying entanglement properties of quantum states and measurements in line networks. The framework is based on the generalised Choi isomorphism, which can be used to map bipartite states and measurements into corresponding quantum operations. We apply the method to networks with trusted end points to demonstrate the power of the approach. We derive bounds for common convex geometric entanglement quantifiers of individual source states, as well as for the network as a whole. We also apply the technique to certification of entanglement dimensionality, proposing the concept of Schmidt number for bipartite measurements in the process. We believe this quantifier can find interest in benchmarking detectors used, e.g. in qutrit teleportation. Applying our formalism further to high-dimensional networks, we derive an activation result for genuinely high-dimensional quantum steering.