AI 中文总结
研究三量子比特CCZ态的设备无关自测试，通过特定的五个上下文关联器确定状态及测量，构造贝尔不等式，利用平方和分解证明量子界，给出两个自测试，表明与通过单个贝尔不等式最大违反识别不同。
AI 中文摘要
三量子比特CCZ态是最小的秩为三的超图态和基本的纠缠魔术资源。其立方相由非泡利串的广义稳定器控制，标准图态自测试论证不直接适用。我们表明，在三方双输入、双输出场景中，从八个全局输入三元组中的五个可获得的二十个关联器，可确定该状态及泡利X/Z测量的作用直至局部等距。证明固定了八个等权重计算分支并在分支立方体上传播条件X翻转关系，恢复111振幅的负号。这五个上下文关联是非局部的，但规范泡利测量不能达到它们违反的任何贝尔不等式的最大量子值。引入独立的第三次测量使基于最大贝尔违反的自测试成为可能。我们构造了一个明确的贝尔不等式，其最大量子违反自测试CCZ态和所有三个局部测量。精确的平方和分解证明了量子界，其等式条件产生解析SWAP提取。这些结果给出了CCZ态的两个明确的设备无关自测试，并表明从几个关联器等式确定一个状态及其测量与通过单个贝尔不等式的最大违反来识别它们是不同的。
英文摘要
The three-qubit CCZ state is the smallest rank-three hypergraph state and an elementary entangled magic resource. Its cubic phase is governed by generalized stabilizers that are not Pauli strings, so standard graph-state self-testing arguments do not apply directly. We show that twenty correlators, all obtainable from five of the eight global input triples in the tripartite two-input, two-output scenario, determine this state and the action of the Pauli $X/Z$ measurements up to local isometries. The proof fixes eight equally weighted computational branches and propagates conditional $X$-flip relations across the branch cube, recovering the minus sign of the $111$ amplitude. These five-context correlations are nonlocal, but the canonical Pauli measurements cannot attain the largest quantum value of any Bell inequality that they violate: whenever they maximize a Bell expression, its local bound has the same value. Introducing an independent third measurement makes self-testing from maximal Bell violation possible. We construct an explicit Bell inequality whose maximal quantum violation self-tests the CCZ state and all three local measurements. An exact sum-of-squares decomposition proves the quantum bound, and its equality conditions yield an analytic SWAP extraction. Together, these results give two explicit device-independent self-tests of the CCZ state and demonstrate that determining a state and its measurements from several correlator equalities is distinct from identifying them through the maximal violation of a single Bell inequality.
Comments26 pages, 2 figures
