Strong notions of nonclassicality: experimental signatures and applications

量子论是大多数现代物理学的基础，但对于它在概念上与经典理论的区别，人们仍然没有达成共识。这不是一个学术问题。在许多任务中——尤其是在密码学和计算方面——量子协议的表现优于经典协议，但对量子理论的糟糕直觉阻碍了我们利用其力量的能力。对于跨学科研究来说，这个问题也很尖锐，因为物理学的不同分支经常使用不同的量子理论公式来定义经典性。最后，在量子效应被认为是重要的新兴领域，如量子生物学和量子机器学习，尚不清楚必须证明什么才能确定给定现象不受经典解释的影响。所有这些都表明，需要一种超越领域和公式的非古典主义统一理论。***一个好的非古典概念也应该是这样的，它可以经受直接的实验检验。这需要能够直接从一组经典原理中推断出实验统计的约束条件。如果一个实验被发现违反了这些约束，那么随之而来的是，在任何能够公正地对待该实验的理论中，必须违反一个或多个原则，包括量子理论的任何未来继承者。换句话说，强烈的非古典主义观念是“经得起未来考验的”。***一个强有力的、统一的非古典主义概念的最好前景是语境性的概念。根据这些观点，一个实验只有在它允许一个非上下文模型的情况下才允许经典解释，这意味着模型中实验过程的表示不依赖于与观察到的统计数据无关的过程的任何特征（称为“上下文”）。非情境性是著名的Kochen-Specker定理的基础，并将贝尔的局部因果关系概念作为一个特例纳入其中。对于各种典型的量子现象，如干涉、隧穿、粒子统计、隐形传态等等，我的目标是精确地确定它们的哪些特征可以被证明是强非经典的。我将开发出对噪声和不完美具有鲁棒性的强非古典性的实验特征的技术。最后，我打算阐明强非经典性是一种资源的意义，特别是为了更好地理解它在信息处理中的应用，并确定它是否适用于其他类型的任务，例如开发高精度传感器或最高效的热机。***参与本研究项目的博士生将深入了解量子的本质及其在未来技术中的潜在应用，为他们在不断发展的量子信息科学领域的职业生涯奠定良好的基础。

Quantum theory underlies most of modern physics, but there is still no consensus about the manner in which it departs conceptually from classical theories. The question is not academic. For many tasks -- in particular in cryptography and computation -- quantum protocols outperform their classical counterparts, but poor intuitions about quantum theory impede our ability to harness its power. The problem is also acute for interdisciplinary research, as different branches of physics often use formulations of quantum theory that differ in their approaches to defining classicality. Finally, in emerging fields where quantum effects are thought to be significant, such as quantum biology and quantum machine learning, it remains unclear what must be demonstrated to establish that a given phenomenon resists classical explanation. All of this points to the need for a unified theory of nonclassicality that transcends fields and formulations. ***A good notion of nonclassicality should also be such that it can be subjected to a direct experimental test. This requires being able to infer constraints on experimental statistics directly from a set of classical principles. If an experiment is found to violate those constraints, then it follows that one or more of the principles must be violated in any theory that can do justice to the experiment, including any future successor to quantum theory. In other words, strong notions of nonclassicality are "future-proof".***The best prospect for a strong and unified notion of nonclassicality is the notion of contextuality. By these lights, an experiment admits of a classical explanation only if it admits of a model that is noncontextual, meaning that the representation of an experimental procedure in the model does not depend on any features of the procedure (termed "contexts") which are irrelevant to the observed statistics. Noncontextuality underlies the famous Kochen-Specker theorem and subsumes Bell's notion of local causality as a special case. For various paradigmatically quantum phenomena, such as interference, tunneling, particle statistics, teleportation, and so forth, I aim to determine precisely which of their features can be proven to be strongly nonclassical. I will develop techniques for deriving experimental signatures of strong nonclassicality that are robust to noise and imperfections. Finally, I intend to elucidate the sense in which strong nonclassicality is a resource, in particular, to better understand its applications to information processing and to determine whether it has applications for other sorts of tasks, such as developing high-precision sensors or optimally efficient heat engines. ***The PhD students working on this research program will acquire a deep understanding of the nature of quantumness and its potential applications to future technologies, positioning them well for careers in the growing field of quantum information science.