Quantumness Via Discrete Structures Demonstrates Contextuality in Multiqubit Systems and Assesses Foundational Departures from Classical Computation
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Quantum mechanics fundamentally differs from classical probability, exhibiting behaviours that promise revolutionary advances in computation and information processing, and researchers are increasingly exploring the role of discrete structures in understanding these quantum phenomena. Ravi Kunjwal, undertaking this research, investigates how mathematical structures like graphs and hypergraphs illuminate core aspects of quantum mechanics, including contextuality, causality, and measurement incompatibility. This work charts a course through these complex areas, revealing connections between abstract mathematical frameworks and the operational limits of quantum technologies, and offering new insights into the very nature of quantum reality. By applying these discrete structures, Kunjwal demonstrates a powerful approach to assessing and synthesizing quantum behaviours, potentially paving the way for more efficient and secure quantum communication and computation. Quantum Foundations, Contextuality and Non-Locality This body of work represents a substantial investigation into the foundations of quantum mechanics, exploring non-locality, contextuality, generalized probabilistic theories, and related areas. Researchers revisited foundational work by Specker, establishing its relevance to modern concepts of contextuality, non-locality, and complementarity. Subsequent studies explored the relationship between incompatibility of measurements and Bell non-locality, demonstrating that incompatibility does not always guarantee non-locality. Investigations into Hardy-type correlations and experimental tests of Bell’s theorem further refined understanding of these fundamental concepts. The research extends beyond standard quantum mechanics, delving into the framework of generalized probabilistic theories (GPTs). Researchers characterized non-classicality within GPTs, exploring accessible fragments of these theories and developing a new branch of entanglement theory. They also developed a resource theory of non-classicality based on common-cause boxes and investigated spacetime entanglement entropy for interacting theories. These studies aim to identify features that distinguish quantum mechanics from classical physics and broaden the scope of quantum information processing. Understanding the limitations of measuring multiple observables simultaneously also received significant attention. Researchers explored almost quantum correlations and their relation to joint measurements, investigating joint measurability relations for qubits and establishing criteria for qubit-realizable structures. These studies contribute to a deeper understanding of the foundations of quantum mechanics and the nature of quantum correlations. Contextuality, Causality and Quantum Computation Links This work presents a comprehensive investigation into the foundations of quantum mechanics, departing from classical probabilistic approaches by exploring the roles of power and computation through discrete structures. Researchers extensively utilized graphs and hypergraphs to analyze contextuality, culminating in insights into generalized contextuality and its operationalization. Specifically, studies of Kochen-Specker contextuality in multiqubit systems revealed connections to quantum computation models. Investigations into causality employed directed graphs, revealing a critical link between indefinite causal order and the limitations imposed by local operations and classical communication, as well as separable operations. This work generalized Bell nonlocality by removing the need for global causal assumptions, establishing a device-independent notion of nonclassicality termed antinomicity. Through collaborations with researchers across Canada, Europe, and the United States, the team supervised numerous students, resulting in a series of publications and presentations at international conferences, consistently advancing the understanding of quantum phenomena and their potential applications.
Discrete Structures Illuminate Quantum Foundations This work presents a comprehensive investigation into the foundations of quantum information processing, departing from classical probabilistic approaches by focusing on the role of discrete structures in assessing and synthesizing quantum phenomena. The research explores contextuality, causality, and the incompatibility of measurements, each leveraging different discrete structures, graphs, directed graphs, and hypergraphs, to model and understand quantum behaviour. Specifically, the team extensively studied Kochen-Specker contextuality and its operationalization, demonstrating its connection to generalized contextuality through hypergraph-theoretic frameworks. Furthermore, the research advances understanding of indefinite causal order, revealing a connection between this concept and the limitations of local operations in quantum communication. A novel notion of nonclassicality, termed antinomicity, was developed, generalizing Bell nonlocality without requiring global causal assumptions. Finally, the team investigated the incompatibility of measurements, demonstrating its relationship to Bell nonlocality and its role in distinguishing between almost quantum correlations, establishing criteria for qubit-realizable joint measurability structures. 👉 More information 🗞 Quantumness via Discrete Structures 🧠 ArXiv: https://arxiv.org/abs/2512.10063 Tags: