This presentation provides a non-technical overview of the notion of quantum superposition of causal structures, of its applications, and of its proposed physical realizations. The conceptual underpinning for these investigations is a view of quantum theory as a new kind of probability theory. At the axiomatic level, the principles of this new kind of probability theory suggest new causal relations that have no analogue in the classical world. These new causal relations are a potential resource for new technologies, including computation and communication technology.
This presentation provides a non-technical overview of the notion of quantum superposition of causal structures, of its applications, and of its proposed physical realizations. The conceptual underpinning for these investigations is a view of quantum theory as a new kind of probability theory. At the axiomatic level, the principles of this new kind of probability theory suggest new causal relations that have no analogue in the classical world. These new causal relations are a potential resource for new technologies, including computation and communication technology.
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
The framework of causal models is ideally suited to formalizing certain conceptual problems in quantum the-ory, and conversely, a variety of tools developed by physicists studying the foundations of quantum theory have applications for causal inference. This talk reviews some of the connections between the two fields. In partic-ular, it is shown that certain correlations predicted by quantum theory and observed experimentally cannot be explained by any causal model while respecting the core principles of causal discovery algorithms. Nonetheless, it is argued that by understanding quantum theory as an innovation to the theory of Bayesian inference, one can introduce a quantum generalization of the notion of a causal model and salvage a causal explanation of these cor-relations without fine-tuning. Furthermore, experiments exhibiting certain quantum features, namely, coherence and entanglement, enable solutions to causal inference problems that are intractable classically. In particular, while passive observation of a pair of variables cannot determine the causal relation that holds between them according to classical physics, this is not the case in quantum physics. In other words, according to quantum theory, certain kinds of correlation do imply causation. The results of a quantum-optical experiment confirming these predictions will be presented. This talk is based on the work described in Refs. [1] and [2].
Recent advances in quantum technology – from quantum computers and simulators to communication and metrology – have not only opened up a whole new world of applications but also changed the understanding of quantum theory itself. This text introduces quantum theory entirely from this new perspective. It does away with the traditional approach to quantum theory as a theory of microscopic matter, and focuses instead on quantum theory as a framework for information processing. Accordingly, the emphasis is on concepts like measurement, probability, statistical correlations, and transformations, rather than waves and particles. The text begins with experimental evidence that forces one to abandon the classical description and to re-examine such basic notions as measurement, probability, and state. Thorough investigation of these concepts leads to the alternative framework of quantum theory. The requisite mathematics is developed and linked to its operational meaning. This part of the text culminates in an exploration of some of the most vexing issues of quantum theory, regarding locality, non-contextuality, and realism. The second half of the text explains how the peculiar features of quantum theory are harnessed to tackle information processing tasks that are intractable or even impossible classically. It provides the tools for understanding and designing the pertinent protocols, and discusses a range of examples representative of current quantum technology.
This research paper delves into the captivating world of quantum superpositioning, tracing its historical evolution, exploring theoretical frameworks, and illuminating a diverse array of applications. From the early conceptions of wave-particle duality to the groundbreaking formulations of Schrödinger's wave equation, quantum superpositioning has emerged as a central theme in the narrative of quantum mechanics. The paper examines the theoretical underpinnings, including the Copenhagen interpretation, the Many-Worlds interpretation, and the intriguing observer effect, unraveling the profound philosophical implications embedded in the fabric of this quantum phenomenon. The practical manifestations of quantum superpositioning are vast and transformative. Quantum computing, with its promise of exponentially faster computations, quantum cryptography ensuring unbreakable communication channels, and quantum sensors pushing the boundaries of precision measurement, showcase the tangible impact of superposition on technology and science. The exploration extends into the realms of quantum communication networks, quantum-enhanced imaging, and quantum-resistant cryptography, providing a comprehensive overview of the diverse applications emerging from the principles of superposition. This paper concludes with a contemplative look toward the future, emphasizing the ongoing challenges and endless possibilities that quantum superpositioning presents. As we navigate through the quantum landscape, the intersections of theory and innovation redefine our understanding of reality and open new frontiers in science and technology. Quantum superpositioning stands as a guiding thread, weaving together the rich tapestry of quantum mechanics, inspiring continued exploration and discovery.
The distinction between classical physics and quantum physics is traditionally analyzed based on concepts such as determinism, the continuous or discrete nature of variables, the non-commutativity of observables, and the superposition of states. This article proposes a more fundamental reinterpretation based on two complementary conceptual ingredients. The first is a minimal relational epistemology, developed from the author's previous work, in which space and time are not a priori frames but emerge from comparisons of movements between systems. The second is an analysis of the role played by the possibility—or impossibility—of defining independent events, a possibility that depends precisely on the prior construction of a spatio-temporal and causal structure. We show that the essential difference between classical physics and quantum physics lies in the rule of probability composition, and not in the features usually invoked. Quantum physics appears to be a coherent description of a physical regime prior to the establishment of the causal independence of events. The two conceptual ingredients are summarized in the form of axioms, broad enough to offer a new perspective on the usual notions of quantum physics, which we review here. Accompanying this text, another article presents more technical developments.