Geometrical self-testing of partially entangled two-qubit states
Geometrical self-testing of partially entangled two-qubit states
复制标题
部分纠缠的两个量子位态的几何自测试
DOI：
10.1088/1367-2630/ab6e49
复制
发表时间：
2020
影响因子：
3.3
通讯作者：
Ishizaka Satoshi
中科院分区：
文献类型：
--
作者：
泉竣;渡邉陽介;Kenji Harada;Ishizaka Satoshi
量子非定域性最近被广泛研究与设备无关的量子信息处理，其中量子相关集合的极值点通过自测试起着至关重要的作用。在大多数协议中，自测试的证明依赖于Bell不等式的最大违反，但还有另一种已知的基于状态向量几何的自测试最大纠缠态的证明。在部分纠缠态的情况下，我们给出了一个几何证明。我们表明，当一组在最简单的贝尔场景的reflectors满足一个条件，状态向量的几何形状是唯一确定的。当几何上存在另一个幺正观测量时，实现就变得可自检验。应用这一事实，我们提出了自我测试协议，故意增加一个测量。这种用于自测试的几何方案是上级的，因为通过将其用作构建块并重复地添加测量，可以自测试具有任意数量的测量的实现。除了应用之外，我们还尝试通过猜测远距离测量结果的概率来描述非局部相关性。在这种描述中，量子集也是凸的，并且一大类极点由几何的唯一性来识别。
Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes self-testable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.