A causal understanding of a physical theory is vital. They provide profound insights into the implications of the theory and contain the information required to manipulate, not only predict, our surroundings. Unfortunately, one of the most broadly used and successful theories, quantum theory, continues to evade a satisfactory causal description. The progress is hindered by the difficulty of faithfully testing causal explanations in an experimental setting. This thesis presents a novel causal discovery algorithm which allows a direct comparison of a wide variety of causal explanations for experimental data. They include causal influences both classical and quantum mechanical in nature. First we provide relevant background information, predominately on quantum mechanics, quantum optics and statistical inference. Next, we review the framework of classical causality and the connection between a causal assumption and statistical model. We then present a novel causal discovery algorithm for noisy experimental data. Finally, we perform two Bell experiments and apply the newly developed algorithm on the resulting data. \nThe causal discovery algorithm operates on observational data without any interven- tions required. It utilizes the concept of predictive accuracy to assign a score to each causal explanation. This allows the simultaneous consideration of classical and quantum causal theories. In addition, this approach allows the identification of overly complex explanations as these perform poorly with respect to this criterion. \nBoth experiments are implemented using quantum optics. The first Bell experiment has a near maximally entangled shared resource state while the second has a separable resource state. The results indicate that a quantum local causal explanation bests describes the first experiment, whereas a classical local causal explanation is preferred for the second. A super-luminal or super-deterministic theory are sub-optimal for both.
A causal understanding of a physical theory is vital. They provide profound insights into the implications of the theory and contain the information required to manipulate, not only predict, our surroundings. Unfortunately, one of the most broadly used and successful theories, quantum theory, continues to evade a satisfactory causal description. The progress is hindered by the difficulty of faithfully testing causal explanations in an experimental setting. This thesis presents a novel causal discovery algorithm which allows a direct comparison of a wide variety of causal explanations for experimental data. They include causal influences both classical and quantum mechanical in nature. First we provide relevant background information, predominately on quantum mechanics, quantum optics and statistical inference. Next, we review the framework of classical causality and the connection between a causal assumption and statistical model. We then present a novel causal discovery algorithm for noisy experimental data. Finally, we perform two Bell experiments and apply the newly developed algorithm on the resulting data. \nThe causal discovery algorithm operates on observational data without any interven- tions required. It utilizes the concept of predictive accuracy to assign a score to each causal explanation. This allows the simultaneous consideration of classical and quantum causal theories. In addition, this approach allows the identification of overly complex explanations as these perform poorly with respect to this criterion. \nBoth experiments are implemented using quantum optics. The first Bell experiment has a near maximally entangled shared resource state while the second has a separable resource state. The results indicate that a quantum local causal explanation bests describes the first experiment, whereas a classical local causal explanation is preferred for the second. A super-luminal or super-deterministic theory are sub-optimal for both.
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].
Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell's local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms , the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.
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.
This thesis details two experimental tests that can be applied to particular quantum states to reveal important information. We begin by discussing the relevant background in quantum information. We introduce qubits and qudits as basic quantum states, and we discuss the evolution and measurement of quantum states. We then discuss quantum state tomography as a means by which to obtain complete information about a state, followed by a discussion of state discrimination as a means by which to determine the state given the promise that it is drawn from some known set. We then discuss relevant experimental techniques in quantum optics, including measurement, generation of entanglement, and generation of single photons from entanglement. \n \nThe first experiment we discuss deals with the causal structure of a system, which is the description of the origin of correlations between two or more states. The causal structure can be direct-cause, meaning that one state causes the other; common-cause, meaning that both states are caused by another; or hybrid-cause, which is a combination of the two. We perform the first implementation of a new type of tomography to determine the causal structure; this is called causal tomography and functions regardless of whether two qubits are related by a common state, a process, or some combination thereof. We implement a process on two entangled photons so that we can select the exact causal structure that results, which ranges continuously between direct-cause and common-cause structures. Using causal tomography, we recover causal structures that closely match expected results and demonstrate that quantum mechanics provides an advantage in causal inference. \n \nThe second experiment we discuss deals with the unambiguous discrimination of multiple quantum states. For the first time, we apply the principles of unambiguous state discrimination to high-dimensional systems. Given a state chosen randomly out of d possible states encoded in d dimensions, we implement a procedure for determining which state was chosen; this procedure in theory functions without error. We encode and detect the states in the orbital angular momentum degree of freedom up to dimension d=14. Although no experiment can provide perfectly error-free measurement due to inevitable imperfections, we obtain an error rate below the theoretical error rate of minimum-error state discrimination for dimensions up to d=12. At the time of submission of this thesis, this work has been accepted for publication in Physical Review Letters.
To date, quantum theory is the most successful physical theory that has been discovered. However, there is still the possibility that an inconsistency between experimental observations and the predictions of quantum theory may one day be found, thus prompting the replacement of quantum theory with a superior, post-quantum theory. To narrow down the scope of possibilities for the true theory that describes nature, one can perform experiments that falsify other physical theories, by demonstrating an incompatibility between experimental observations and the predictions of these theories. This thesis details two such experiments. First we provide relevant background information, beginning with a review of experimental quantum optics. Next, we review noncontextual ontological theories and discuss requirements for experimental tests of such theories. Finally, we discuss the framework of generalised probabilistic theories before introducing the two experiments. \n \n \nThe first experiment is a test of noncontextual ontological (or hidden-variable) models of nature. An ontological model of a physical theory is one in which systems have preexisting properties, and a noncontextual ontological model is one in which systems that are indistinguishable experimentally are represented identically in the model. Physical theories that cannot be represented by a noncontextual ontological model are said to be nonclassical; quantum theory is an example of such a physical theory that is nonclassical in this sense. Prior to this thesis, experimental tests of the assumption of noncontextuality had assumed that the experiments were free of both systematic and statistical errors, which is not justifiable for any experiment. We introduce new analytical techniques that allow us to avoid making these assumptions, and perform an experiment with single photons that, with high confidence, rules out the possibility of describing nature with a noncontextual ontological model. \n \n \nThe second experiment is a demonstration of self-consistent state and measurement tomography in the framework of generalised probabilistic theories (GPTs). The GPT framework is a very general, operationally-motivated framework for describing a physical theory in terms of the observable events predicted by the theory. We develop a technique for inferring the GPT description of a set of states and measurements directly from experimental data. By analysing our data in this general framework, we are able to test various candidate physical theories of nature. We perform an experiment with single photons, and quantify the size of possible variations between quantum theory and the true physical theory that describes nature.