Certification of a functionality in a quantum network stage

We consider testing the ability of quantum network nodes to execute multi-round quantum protocols. Specifically, we examine protocols in which the nodes are capable of performing quantum gates, storing qubits and exchanging said qubits over the network a certain number of times. We propose a simple ping-pong test, which provides a certificate for the capability of the nodes to run certain multi-round protocols. We first show that in the noise-free regime the only way the nodes can pass the test is if they do indeed possess the desired capabilities. We then proceed to consider the case where operations are noisy, and provide an initial analysis showing how our test can be used to estimate parameters that allow us to draw conclusions about the actual performance of such protocols on the tested nodes. Finally, we investigate the tightness of this analysis using example cases in a numerical simulation.