Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell's notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality.
Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell's notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality.
A key aim of quantum foundations is to characterize the sense in which nature goes beyond classical physics. Understanding nonclassicality is one of our best avenues towards finding a satisfactory interpretation of quantum theory. By determining which classical principles cannot be satisfied in any empirically adequate physical theory, we begin to see which principles can be preserved, which in turn gives us insight into the ontology of the world. These insights then guide us in determining which questions to ask and which experiments to perform next. Furthermore, it is these nonclassical aspects of nature that give rise to new technologies such as the speed-ups of quantum computation or the security of quantum key distribution. \n \nThe gold standard for establishing that a phenomenon is truly nonclassical is to prove that it violates the principle of local causality or the principle of noncontextuality. Much of this thesis reports on my research relating to these two principles. This research primarily involves (i) finding new justifications for our notions of nonclassicality; (ii) refining their fundamental definitions; (iii) quantifying and characterizing their various manifestations; and (iv) finding applications where nonclassical phenomena act as resources for information processing. \n \nUltimately, all of this work on nonclassicality is woven together into a novel framework for physical theories introduced by myself, John Selby, and Rob Spekkens. Its main advantage over preexisting frameworks is that it maintains a clear distinction between which elements of a given physical theory directly describe causal processes, and which refer only to one’s inferences about causal processes. This clarifies a number of confusions in the literature which arose precisely because previous frameworks scrambled causal and inferential concepts. Furthermore, local causality and noncontextuality emerge in this framework as the assumptions that the causal and inferential structures (respectively) that are operationally observed must be respected in the underlying ontology. This work constitutes a first step in developing a new interpretation of quantum theory—the first interpretation designed to satisfy the spirit of both local causality and noncontextuality.
Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. Realism is here formalized by the ontological models framework, where elements of reality are points of a measurable space and probabilities obey the Kolmogorov axioms. In the Bell scenario, locally causal ontological models posit a common cause supporting a global valuation, a joint assignment of outcomes to all measurements at once, across incompatible contexts. Within this notion of realism, Bell's theorem makes any realist explanation of the quantum predictions conspiratorial: any mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest operationally. We redefine realism through a new ontological framework that generalizes the standard one. The elements of reality, which we call records, are no longer points but relational parts of a point-free generalization of a topological space (sublocales of a locale). A record shared by two incompatible contexts establishes the sameness of a measurement across them, without such pairwise identities composing into a global valuation, and the common cause is then a web of such records. Within this framework, Bell's no-go theorem becomes a go theorem: local causality, restated for records, is no longer at odds with the quantum statistics. This is possible because modularity, the inclusion-exclusion law of classical probability, fails across incompatible contexts, so that the probability theory generalizes Kolmogorov's. We exhibit explicit models reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell-CHSH value up to the algebraic maximum. A realist explanation of the quantum predictions need not be conspiratorial; every causal influence posited by these models is reflected in the operational predictions.
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].
In quantum mechanics, quantum nonseparability is at the core of philosophical debates regarding its meaning. In the context of the process matrix formalism, causal nonseparability characterises quantum processes (connecting the inputs and outputs of different local quantum operations) that are incompatible with any definite causal structure among interacting parties. One talks about indefinite causal orders. A famous example of causally nonseparable processes is called the quantum switch (QS). It is extensively studied in the literature in virtue of its simple architecture and its various implementations in laboratories.The present work will discuss the possible interpretations of the QS's causal nonseparability under the assumption that causal nonseparability is seen as pointing towards novel objective features of nature.It was first defended that a scientific realist approach towards the process matrix formalism, which is an operational theory generalising quantum mechanics, was as much legitimate as any possible antirealist reading, contrary to certain views found in the literature. The reason is that operational formalisms are ontologically and epistemically neutral.From there, the theoretical concepts of interest, namely causal nonseparability and its model-independent counterpart called noncausality, were analysed in more details, in order to highlight in what sense they are distinct from the standard notions of quantum nonseparability and nonlocality in quantum mechanics.The discussion then focused on noncausality. It was argued that noncausality has a strong connection with a notion of temporal nonlocality. In the same way that Bell nonlocality is given different underlying explanations depending on the details of the chosen quantum mechanics' account, noncausality pointing towards temporal nonlocality can be given a variety of underlying descriptions depending on the exact way to interpret the process matrix formalism.The last chapter focused precisely on this particular point, namely on the various ways to understand process matrices and causal nonseparability in a realist context. In order to explore the potential impact of causal nonseparability on spacetime,we shifted from the notion of (indefinite) causal structure to (indefinite) spatiotemporal ones. This shift was allowed under a set of reasonable assumptions regarding the properties of a physical spacetime manifold and the connection between an operational and relativistic notions of causal relations.While different readings were suggested for indefiniteness of spatiotemporal relations, we insisted in particular on an objective understanding appealing to the concept of metaphysical indeterminacy. It was argued that such an approach could prove useful in a more general theoretical context such as quantum gravity, while being already partly supported in standard quantum mechanics.
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or “ontology”, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real—that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach’s principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach’s principle). This new definition of quantum causal models is illustrated by examples and strengthened by it’s foundation on a robust quantum Reichenbach’s principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. While the framework has been generalized in a variety of different ways to the quantum case, much of this work leaves open whether causal concepts are fundamental to quantum theory, or only find application at an emergent level of classical devices and measurement outcomes. Here, we present a framework of quantum causal models, with causal relations defined in terms intrinsic to quantum theory, and the central object of study being the quantum process itself. Following Allen et al., Phys. Rev. X 7, 031021 (2017), the approach defines quantum causal relations in terms of unitary evolution, in a way analogous to an approach to classical causal models that assumes underlying determinism and situates causal relations in functional dependences between variables. We show that any unitary quantum circuit has a causal structure corresponding to a directed acyclic graph, and that when marginalising over local noise sources, the resulting quantum process satisfies a Markov condition with respect to the graph. We also prove a converse to this statement. We introduce an intrinsically quantum notion that plays a role analogous to the conditional independence of classical variables, and (generalizing a central theorem of the classical framework) show that d-separation is sound and complete for it in the quantum case. We present generalizations of the three rules of the classical do-calculus, in each case relating a property of the causal structure to a formal property of the quantum process, and to an operational statement concerning the outcomes of interventions. In addition, we introduce and derive similar results for classical split-node causal models, which are more closely analogous to quantum causal models than the classical causal models that are usually studied.