Discrimination between objects, in particular quantum states, is one of the most fundamental tasks in (quantum) information theory. Recent years have seen significant progress towards extending the framework to point-to-point quantum channels. However, with technological progress the focus of the field is shifting to more complex structures: Quantum networks. In contrast to channels, networks allow for intermediate access points where information can be received, processed and reintroduced into the network. In this work we study the discrimination of quantum networks and its fundamental limitations. In particular when multiple uses of the network are at hand, the rooster of available strategies becomes increasingly complex. The simplest quantum network that capturers the structure of the problem is given by a quantum superchannel. We discuss the available classes of strategies when considering $n$ copies of a superchannel and give fundamental bounds on the asymptotically achievable rates in an asymmetric discrimination setting. Furthermore, we discuss achievability, symmetric network discrimination, the strong converse exponent, generalization to arbitrary quantum networks and finally an application to an active version of the quantum illumination problem.

翻译：对象区分，尤其是量子态的区分，是（量子）信息理论中最基础的任务之一。近年来，将该框架扩展至点对点量子信道的研究取得了显著进展。然而，随着技术进步，该领域的焦点正转向更为复杂的结构——量子网络。与信道不同，网络允许信息在其中间接入点被接收、处理并重新注入网络。本文研究量子网络的区分及其基本限制。特别地，当网络可被多次使用时，可用策略的复杂性随之增加。能捕捉该问题结构的最简量子网络由量子超信道给出。我们探讨了考虑$n$个超信道副本时可用的策略类别，并给出了非对称区分场景下渐近可达速率的基本界限。此外，我们还讨论了可实现性、对称网络区分、强逆指数、对任意量子网络的泛化，最终将其应用于量子照明问题的主动版本。