Khrennikov Andrei
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden.
Entropy (Basel). 2022 Sep 28;24(10):1380. doi: 10.3390/e24101380.
This is a review devoted to the complementarity-contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. is the dependence of an observable's outcome on the experimental context; on the system-apparatus interaction. Probabilistically, complementarity means that the (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called (JMC), the special case of Bohr's contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling-for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of "pure contextuality" from data shadowed by signaling. This theory is known as (CbD). It leads to inequalities with an additional term quantifying signaling: Bell-Dzhafarov-Kujala inequalities.
这是一篇致力于探讨互补性与语境性相互作用以及与贝尔不等式关联的综述。从互补性开始讨论，我指出语境性是其根源。语境性是指可观测量的结果依赖于实验语境，即系统与仪器的相互作用。从概率角度来看，互补性意味着联合概率分布（JPD）不存在。取而代之的是，人们必须运用语境概率。贝尔不等式被解释为对语境性的统计检验，进而也是对不相容性的检验。对于依赖语境的概率，这些不等式可能会被违反。我强调，由贝尔不等式检验的语境性是所谓的联合测量语境性（JMC），它是玻尔语境性的特殊情况。然后，我考察信号传递（边际不一致性）的作用。在量子力学中，信号传递可被视为一种实验假象。然而，实验数据常常呈现出信号传递模式。我讨论了信号传递的可能来源，例如态制备对测量设置的依赖。原则上，人们可以从被信号传递掩盖的数据中提取“纯语境性”的度量。这一理论被称为语境性引导（CbD）。它导出了带有一个量化信号传递的附加项的不等式：贝尔 - 贾法罗夫 - 库贾拉不等式。
