Strong notions of nonclassicality: experimental signatures and applications

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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.