A review is made of the field of contextuality in quantum mechanics. We study the historical emergence of the concept from philosophical and logical issues. We present and compare the main theoretical frameworks that have been derived. Finally, we focus on the complex task of establishing experimental tests of contextuality. Throughout this work, we try to show that the conceptualisation of contextuality has progressed through different complementary perspectives, before summoning them together to analyse the signification of contextuality experiments. Doing so, we argue that contextuality emerged as a discrete logical problem and developed into a quantifiable quantum resource.
A review is made of the field of contextuality in quantum mechanics. We study the historical emergence of the concept from philosophical and logical issues. We present and compare the main theoretical frameworks that have been derived. Finally, we focus on the complex task of establishing experimental tests of contextuality. Throughout this work, we try to show that the conceptualisation of contextuality has progressed through different complementary perspectives, before summoning them together to analyse the signification of contextuality experiments. Doing so, we argue that contextuality emerged as a discrete logical problem and developed into a quantifiable quantum resource.
The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden-variable theory. It is shown that such a hidden-variable description can be viewed as either contextual in the random variables mapping hidden states to observable outcomes or in the probability measure on the hidden state space. The latter view suggests that this apparent contextuality may be interpreted as a simple consequence of measurement disturbance, wherein the initial hidden state is altered through interaction with the measuring device, thereby giving rise to a possibly different final hidden-variable state from which the measurement outcome is obtained. In light of this observation, a less restrictive and, arguably, more reasonable definition of noncontextuality is suggested. To prove that such a description is possible, an explicit and, in this sense, noncontextual hidden-variable model is constructed, which reproduces all quantum theoretic predictions for the Mermin-Peres square. A critical analysis of some recent and proposed experimental tests of contextuality is also provided. Although the discussion is restricted to a four-dimensional Hilbert space, the approach and conclusions are expected to generalize to any Hilbert space.
Entanglement and contextuality are among the most intriguing and fundamental features of quantum mechanics. Entanglement concerns quantum states:it is a phenomenon that happens when a system can not be described by the knowledge of its subparts. Contextuality concerns quantum observables: it is the capacity they have to give rise to different experimental results depending on the observables with which they are measured. Both have received tremendous attention during the last decades, following the second quantum revolution, that saw the attitude towards quantum features switch from "why is that so?" to "how can we use this?".This thesis conceives protocols to detect and characterise entanglement and contextuality in specific setups, seeking to fill the gaps between the theoretical studies and the experimental implementations. Entanglement is studied in the case of optical hybrid variables, a recent approach that tries to join the advantages of the discrete and continuous variables encoding of information for quantum communication and computation protocols. In a first chapter, we study how the formalism of matrices of moments can be adapted to the hybrid case and apply it to several hybrid entangled states. We then explore various possible improvements and refinements using the theory of positive maps, in order to gain sensitivity with regard to our detection thresholds. In a second chapter, we focus on a specific setup, define an entanglement witness and explain how it can be implemented on available experiments. It is robust to noise currently observed in quantum optical setups and is based on measurements of genuinely hybrid observables. Contextuality is studied in a last part. A review is made of the theory, from its emergence through philosophical questions to the first mathematical proofs that quantum mechanics is contextual. The main structural theories that yield a global approach to this concept are presented. They are summoned to understand and discuss the loopholes that can affect experiments of contextuality. A protocol is given for a much-studied experiment, that of the Peres-Mermin square.
Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a universal framework for quantifying contextuality. We conduct two complementary approaches: (i) the bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) the top-down approach, where we just postulate two measures, relative entropy of contextuality and contextuality cost, analogous to existent measures of nonlocality (a special case of contextuality). We then match the two approaches by showing that the measure emerging from the communication scenario turns out to be equal to the relative entropy of contextuality. Our framework allows for the quantitative, resource-type comparison of completely different games. We give analytical formulas for the proposed measures for some contextual systems, showing in particular that the Peres-Mermin game is by order of magnitude more contextual than that of Klyachko et al. Furthermore, we explore properties of these measures such as monotonicity or additivity.
In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution, we review recent developments towards a resource theory of contextuality and connections with operational applications of this property. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.
Abstract Open-access, online quantum computers have shown significant improvements in the past decade. Although they still suffer from noise and scalability limitations, they do offer the possibility of experimenting with quantum circuits which would otherwise have required laboratory resources and prowesses beyond the reach of most students (and even researchers). In view of this, we revisit from the ground up the notion of contextuality and show that it can now be easily demonstrated on one of the IBM quantum computers. We showcase this with an implementation of the Peres–Mermin square which, despite the high error rates, manages to violate noncontextuality by almost 28 standard deviations.