The goal of quantum network tomography (QNT) is the characterization of internal quantum channels in a quantum network from external peripheral operations. Prior research has primarily focused on star networks featuring bit-flip and depolarizing channels, leaving the broader problem -- such as QNT for networks with arbitrary topologies and general Pauli channels -- largely unexplored. Moreover, establishing channel identifiability remains a significant challenge even in simplified quantum star networks. In the first part of this paper, we introduce a novel network tomography method, termed Mergecast, in quantum networks. We demonstrate that Mergecast, together with a progressive etching procedure, enables the unique identification of all internal quantum channels in networks characterized by arbitrary topologies and Pauli channels. As a side contribution, we introduce a subclass of Pauli channels, termed bypassable Pauli channels, and propose a more efficient unicast-based tomography method, called BypassUnicast, for networks exclusively comprising these channels. In the second part, we extend our investigation to a more realistic QNT scenario that incorporates state preparation and measurement (SPAM) errors. We rigorously formulate SPAM errors in QNT, propose estimation protocols for such errors within QNT, and subsequently adapt our Mergecast approaches to handle networks affected by SPAM errors. Lastly, we conduct NetSquid-based simulations to corroborate the effectiveness of our proposed protocols in identifying internal quantum channels and estimating SPAM errors in quantum networks. In particular, we demonstrate that Mergecast maintains good performance under realistic conditions, such as photon loss and quantum memory decoherence.

翻译：量子网络层析成像（QNT）的目标是通过外部外围操作来表征量子网络内部的量子信道。先前的研究主要集中于具有比特翻转信道和去极化信道的星型网络，而更广泛的问题——例如针对任意拓扑结构和一般泡利信道的量子网络层析成像——在很大程度上尚未得到探索。即使在简化的量子星型网络中，建立信道的可辨识性仍然是一个重大挑战。在本文的第一部分，我们提出了一种名为Mergecast的新型量子网络层析成像方法。我们证明，Mergecast结合渐进蚀刻过程，能够唯一地识别具有任意拓扑结构和泡利信道特征网络中的所有内部量子信道。作为一项附带贡献，我们引入了一类称为可旁路泡利信道的泡利信道子类，并针对仅包含此类信道的网络，提出了一种更高效的基于单播的层析成像方法，称为BypassUnicast。在第二部分，我们将研究扩展至包含状态制备与测量（SPAM）误差的更现实的量子网络层析成像场景。我们严格形式化了量子网络层析成像中的SPAM误差，提出了在此框架下估计此类误差的协议，并随后调整了我们的Mergecast方法以处理受SPAM误差影响的网络。最后，我们基于NetSquid进行仿真，以验证所提协议在识别量子网络内部量子信道及估计SPAM误差方面的有效性。特别地，我们证明了Mergecast在光子损耗和量子存储器退相干等现实条件下仍能保持良好的性能。