论文标题
非上下文性不平等和量子设备的自我测试的平方分解总和分解
Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
论文作者
论文摘要
违反非上下文性不平等或称为“量子上下文性”的现象是量子理论的基本特征。在本文中，我们在最简单的（奇怪的）顺序测量场景中得出了一个新的非上下文性不平等的家族，以及它们的平衡总和分解，能够展示Kochen-Specker上下文。平方分解的总和使我们能够获得对这些不平等的最大量子违反，并且一组代数关系必然被任何状态所满足，并实现了它。在他们的帮助下，我们证明我们的不平等现象可用于自我测试三维量子状态和测量。值得注意的是，提出的自我测试结果依赖于对测量设备的单一假设，该假设比Kochen-Specker上下文中考虑的假设要弱得多。
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on a single assumption about the measurement device that is much weaker than the assumptions considered in Kochen-Specker contextuality.
