发表机构
Aix-Marseille University, CNRS, LIS（艾克斯-马赛大学，法国国家科学研究中心，实验室信息学、信号与自动控制研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明稳定化乘积基中的态可被完美区分当且仅当对应过程函数违反因果不等式，赋予因果不等式违反以非稳定化资源见证的新操作性意义。
AI 中文摘要
稳定化操作描述了量子理论的一个片段，由于 Gottesman-Knill 定理，该片段已知可被经典高效模拟。因此，非稳定化资源（如魔法态）对于通用量子计算是必要的。有趣的是，魔法资源理论的操作性方法与公理化方法有所不同：前者中的自由操作集，即稳定化操作（SO），严格小于后者中的自由操作集，即完全保持稳定化的操作（CSPO）。展示这种分离的一个简单例子是由一个三量子比特稳定化乘积基给出，其态无法使用 SO 完美区分，但使用 CSPO 却可以完美区分。这样的态系被称为表现出无魔法的非稳定化资源（NSWM）。在此，我们获得了对这一现象的原理性理解，证明了其存在的必要且充分条件。我们首先推导出一个简单判据，以决定给定一个稳定化基，其态是否可仅使用稳定化操作完美区分。然后，我们考虑稳定化基仅包含乘积态的情况，并利用其与过程函数（无悖论因果环的经典模型）的联系，证明以下结论：稳定化乘积基中的态需要非稳定化资源才能完美区分，当且仅当相应的过程函数违反因果不等式。这为因果不等式违反作为非稳定化资源的见证提供了新的操作性意义，这是一种计算非经典性的形式。
英文摘要
Stabilizer operations describe a fragment of quantum theory that is known to be efficiently classically simulable, thanks to the Gottesman-Knill theorem. For this reason, nonstabilizer resources such as magic states are necessary for universal quantum computation. Interestingly, the operational and axiomatic approaches to the resource theory of magic differ: the set of free operations in the former, namely, stabilizer operations (SO), is strictly smaller than that in the latter, namely, completely stabilizer preserving operations (CSPO). A simple example showing the separation is given by a three-qubit stabilizer product basis whose states cannot be perfectly discriminated using SO, but which do admit perfect discrimination using CSPO. Such an ensemble of states is said to exhibit nonstabilizerness without magic (NSWM). Here we obtain a principled understanding of this phenomenon, proving necessary and sufficient conditions for its existence. We first derive a simple criterion to decide whether, given a stabilizer basis, its states can be perfectly discriminated using stabilizer operations alone. We then consider the case where the stabilizer basis contains only product states and use its link with process functions---classical models of paradox-free causal loops---to prove the following: the states in a stabilizer product basis require nonstabilizerness for perfect discrimination if and only if the corresponding process function violates a causal inequality. This provides a new operational meaning to causal inequality violations as witnesses of nonstabilizerness, a form of computational nonclassicality.
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