Xu Zhen-Peng, Chen Jing-Ling, Gühne Otfried
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China.
Phys Rev Lett. 2020 Jun 12;124(23):230401. doi: 10.1103/PhysRevLett.124.230401.
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [Phys. Lett. A 212, 183 (1996)PYLAAG0375-960110.1016/0375-9601(96)00134-X] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.
量子力学基础中的一个核心成果是科亨 - 施佩克尔定理。简而言之，该定理表明量子力学无法与针对理想测量而言非情境性的经典模型相协调。科亨和施佩克尔的首次明确推导相当复杂，但此后已实现了相当大的简化。我们提出一种系统方法来寻找科亨 - 施佩克尔定理的最小哈迪型和格林伯格 - 霍恩 - 泽林格型（GHZ型）证明，其特征在于经典模型的预测与量子力学的预测相反。基于我们的结果，我们表明来自卡贝洛等人[《物理快报A》212, 183 (1996)PYLAAG0375 - 960110.1016/0375 - 9601(96)00134 - X]的具有18个向量的科亨 - 施佩克尔集是任何维度下的最小集，证实了佩雷斯的一个长期猜想。我们的结果有助于识别最小情境性场景并研究它们在信息处理中的有用性。
