论文标题
佩雷斯猜想的证据
Proof of the Peres conjecture for contextuality
论文作者
论文摘要
量子力学基础的核心结果是Kochen-Specker定理。简而言之，它指出，量子力学不能与理想测量的不副本的经典模型进行调和。 Kochen和Specker的第一个显式推导非常复杂，但是此后已经实现了相当大的简化。我们提出了一种系统的方法，可以找到最小的硬质类型和Greenberger-Horne-Zeilinger-type（GHz-type）对Kochen-Specker定理的证明，这些证明的特征是，经典模型的预测与量子力学的预测相反。根据我们的结果，我们证明了Kochen-Specker设置了Cabello等人的18个矢量。 [一个。 Cabello等人，物理。 Lett。 A 212，183（1996）]是任何维度的最小设置，可以通过佩雷斯进行长期的猜想。我们的结果允许确定最小的上下文情景，并研究其对信息处理的有用性。
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. [A. Cabello et al., Phys. Lett. A 212, 183 (1996)] 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.
