Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a non-classical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property of non-signalling or non-disturbance, and the latter by the empirical property of measurement sharpness. However, in realistic experiments neither empirical property holds exactly, which leads to possible objections to contextuality as a form of non-classicality, and potential vulnerabilities for supposed quantum advantages. We introduce measures to quantify both properties, and introduce quantified relaxations of the corresponding assumptions. We prove the continuity of a known measure of contextuality, the contextual fraction, which ensures its robustness to noise. We then bound the extent to which these relaxations can account for contextuality, via corrections terms to the contextual fraction (or to any non-contextuality inequality), culminating in a notion of genuine contextuality, which is robust to experimental imperfections. We then show that our result is general enough to apply or relate to a variety of established results and experimental set-ups. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

中文翻译：

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修正了贝尔和非上下文不等式以进行实际实验

上下文性是量子相关性的一个特征。从基础角度来看，作为一种非经典现象，从应用角度来看，它作为量子优势的资源，至关重要。它通常用隐藏变量来定义，这与参数独立性和决定论的假设相矛盾。前者可以通过无信号或无干扰的经验特性来证明，而后者可以通过测量清晰度的经验特性来证明。然而，在现实实验中，这两种经验性质都不完全成立，这可能会导致对作为一种非经典性形式的情境性的反对，以及所谓的量子优势的潜在脆弱性。我们引入了量化这两个属性的措施，并引入了相应假设的量化松弛。我们证明了已知的上下文度量（上下文分数）的连续性，这确保了其对噪声的鲁棒性。然后，我们通过对上下文分数（或任何非上下文不等式）的修正项来限制这些松弛可以解释上下文的程度，最终得出真正的上下文概念，该概念对实验缺陷具有鲁棒性。然后，我们表明我们的结果足够通用，可以应用或与各种已建立的结果和实验设置相关。本文是“量子背景、因果关系和选择自由”主题的一部分。