Anonymous transmission in a noisy quantum network using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>W</mml:mi></mml:math> state

We consider the task of anonymously transmitting a quantum message in a network. We present a protocol that accomplishes this task using the $W$ state and we analyze its performance in a quantum network where some form of noise is present. We then compare the performance of our protocol with some of the existing protocols developed for the task of anonymous transmission. We show that, in many regimes, our protocol tolerates more noise and achieves higher fidelities of the transmitted quantum message than the other ones. Furthermore, we demonstrate that our protocol tolerates one nonresponsive node. We prove the security of our protocol in a semiactive adversary scenario, meaning that we consider an active adversary and a trusted source.