如何提高经典可模拟测量的区分能力？
How to improve the discrimination power of classically simulable measurements?
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中文总结 AI 辅助
研究如何提高经典可模拟测量（CSMs）的区分能力，考虑添加魔法资源、使用量子催化剂和量子存储器三种方法，通过关联测量与通道转化问题，推导出模拟成本上下界，给出界重合例子，还建立不可行定理表明某些情况下无法提高区分最优成功率。
中文摘要 AI 辅助
经典可模拟测量（CSMs）是奇素数维魔法资源理论中一类重要的受限测量，指具有正离散维格纳函数的测量。因其区分能力弱于全局测量，所以研究如何提高CSMs的区分能力很有必要。本文考虑了三种提高CSMs区分能力的方法，包括添加魔法资源、使用量子催化剂和使用量子存储器。具体而言，将具有正离散维格纳函数的测量与完全正定的维格纳保持测量通道相关联，把提高CSMs区分能力的问题转化为确定使用自由操作模拟量子通道所需魔法资源数量的问题。基于此，推导出模拟成本的上下界。此外，给出了这些界重合的具体例子，并证明消耗性魔法资源可增强CSMs的区分能力。最后，建立了一个不可行定理，表明对于区分一对具有正维格纳函数的态，有限维量子催化剂和有限维量子存储器都不能提高使用CSMs进行区分的最优成功概率。
英文摘要
Classically simulable measurements (CSMs) constitute an important class of restricted measurements in the odd-prime-dimensional magic resource theory, referring to those measurements with positive discrete Wigner functions. Since their discrimination power is weaker than that of global measurements, it is necessary to study how to improve the discrimination power of CSMs. In this paper, we consider three methods to improve the discrimination power of CSMs, including adding magic resources, using quantum catalysts, and using quantum memories. Specifically, we relate measurements with positive discrete Wigner functions to completely positive Wigner-preserving measurement channels, thereby transforming the problem of improving the discrimination power of CSMs into the problem of determining how many magic resources are required to simulate quantum channels using free operations. Based on this, we derive the lower and upper bounds of the simulation cost. Moreover, we provide a concrete example for which these bounds coincide and prove that consumable magic resources can enhance the discrimination power of CSMs. Finally, we establish a no-go theorem, which shows that for discriminating a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination using CSMs.
