发表机构
The Hong Kong University of Science and Technology (Guangzhou); Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area; The University of Hong Kong（香港科技大学（广州）; 粤港澳大湾区量子科学中心; 香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究相干资源理论下高阶量子变换的因果架构影响，证明振幅阻尼信道存在严格因果层级，而混合泡利信道因程序态并行化可实现相同最优误差。
AI 中文摘要
高阶量子变换允许通过不同的因果架构组合多次信道使用，从并行和固定顺序的序列网络到一般的高阶过程。当高阶操作同时受资源理论约束时，这种因果自由度是否能够改善信道变换，在很大程度上仍未得到探索。我们在相干性的动力学资源理论中，使用统一的半定规划框架研究了这一问题。对于两个量子比特的振幅阻尼信道和恒等目标，我们证明了在最大非相干超信道（MISC）和退相协变非相干超信道（DISC）下，在每一个非平凡的阻尼强度下都存在严格的因果层级。相比之下，混合泡利信道允许一种共同的隐形传态模拟，该模拟将信道依赖性转移到并行制备的贝尔对角程序态上。剩余的处理可以被吸收到单个量子操作中，因此并行、固定顺序序列和一般高阶策略对于任何目标都能达到相同的最优误差。这些结果将自由程序态并行化识别为因果增强的结构性障碍。
英文摘要
Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.
Comments31+13 pages, 2 figures
