论文标题
不兼容与钟声之间的定性等效性
Qualitative equivalence between incompatibility and Bell nonlocality
论文作者
论文摘要
量子理论中的测量可能无法共同测量。像纠缠一样，这种测量不兼容是必要的，但不足以违反贝尔的不平等现象。一组测量之间的兼容性关系可以用联合测量性结构表示，即，超图表示，其顶点表示测量和Hyperedges表示所有兼容的测量集。由于违反钟形的不兼容性是必要的，因此钟形实验每个机翼上的关节可测量结构必须不仅仅是不平凡的，即，它必须接受不相容的顶点的子集。在这里，我们表明，对于具有有限的顶点的任何非平凡的连接性可测量结构，都存在量子实现，并进行了一组测量值，可以使铃铛违规，即，鉴于Alice可以访问这套不相容的测量值，因此存在对Bob和它们之间共享的一系列衡量标准，它们可以共享这些贝尔之间的贝尔，而它们可能会违反贝尔。因此，非平凡的关节可测量性结构不仅需要违反铃铛，而且还足够。
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of measurements can be represented by a joint measurability structure, i.e., a hypergraph whose vertices denote measurements and hyperedges denote all and only compatible sets of measurements. Since incompatibility is necessary for a Bell violation, the joint measurability structure on each wing of a Bell experiment must necessarily be non-trivial, i.e., it must admit a subset of incompatible vertices. Here we show that for any non-trivial joint measurability structure with a finite set of vertices, there exists a quantum realization with a set of measurements that enables a Bell violation, i.e., given that Alice has access to this incompatible set of measurements, there exists a set of measurements for Bob and an entangled state shared between them such that they can jointly violate a Bell inequality. Hence, a non-trivial joint measurability structure is not only necessary for a Bell violation, but also sufficient.
