Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause and effect, implying that tools and concepts developed over the years having in mind a classical world have to be reevaluated in the presence of quantum effects. Here, we propose the quantum version of the most common causality quantifier, the average causal effect, measuring how much a target quantum system is changed by interventions on its presumed cause. Not only does it offer an innate manner to quantify causation in two-qubit gates but also in alternative quantum computation models such as the measurement-based version, suggesting that causality can be used as a proxy for optimizing quantum algorithms. Considering quantum teleportation, we show that any pure entangled state offers an advantage in terms of causal effects as compared to separable states. This broadness of different uses showcases that, just as in the classical case, the quantification of causal influence has foundational and applied consequences and can lead to a yet totally unexplored tool for quantum information science.
Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause and effect, implying that tools and concepts developed over the years having in mind a classical world have to be reevaluated in the presence of quantum effects. Here, we propose the quantum version of the most common causality quantifier, the average causal effect, measuring how much a target quantum system is changed by interventions on its presumed cause. Not only does it offer an innate manner to quantify causation in two-qubit gates but also in alternative quantum computation models such as the measurement-based version, suggesting that causality can be used as a proxy for optimizing quantum algorithms. Considering quantum teleportation, we show that any pure entangled state offers an advantage in terms of causal effects as compared to separable states. This broadness of different uses showcases that, just as in the classical case, the quantification of causal influence has foundational and applied consequences and can lead to a yet totally unexplored tool for quantum information science.
Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question, we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even postquantum nature of a common cause. In particular, by considering the simplest instrumental scenario-for which violation of Bell inequalities is not possible-we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus, answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.
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].
We introduce two quantitative measures of the strength of causal relations in quantum theory and more general physical theories. These two measures, called the maximum and minimum causal effect, quantify the maximum and minimum changes in the output of a quantum process induced by changes in its input. The maximum and minimum causal effect possesses useful properties, such as continuity and data-processing inequality. In quantum theory, they have close connections with quantum information tasks. The maximum quantum causal effect can be used to detect quantum channels with nonzero capacity for transmitting classical information. The minimum causal effect can be used to guarantee the recoverability of quantum information: every quantum process with a high value of the minimum quantum causal effect can be approximately inverted. Moreover, we show that the quantum causal effects satisfy a duality relation: if the minimum causal effect of a quantum system A on another quantum system B is high, then A must have a low value of the maximum causal effect on any other quantum system B ′ that is spacelike separated with B . This duality implies a monogamy relation for quantum causal effects, and represents a fundamental difference between quantum and classical causal relations. We illustrate the application of the maximum causal effect to the analysis of two paradigmatic examples, the first involving a coherent superposition of direct cause and common cause, and the second involving a coherent superposition of multiple quantum processes.
Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and the conditional mutual information of observed variables to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. As an application, we consider a system of three entangled qubits and transmit the second and third qubits over separate noisy quantum channels. In this model, we validate that the first qubit is a latent confounder and the common cause of the second and third qubits. In contrast, when two entangled qubits are prepared and one of them is sent over a noisy channel, there is no common confounder. We also demonstrate that the proposed approach outperforms the results of classical causal inference for the Tubingen database when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions. Thus, the proposed approach unifies classical and quantum causal inference in a principled way.
It is a relatively new insight of classical statistics that empirical data can contain information about causation rather than mere correlation. First algorithms have been proposed that are capable of testing whether a presumed causal relationship is compatible with an observed distribution. However, no systematic method is known for treating such problems in a way that generalizes to quantum systems. Here, we describe a general algorithm for computing information–theoretic constraints on the correlations that can arise from a given causal structure, where we allow for quantum systems as well as classical random variables. The general technique is applied to two relevant cases: first, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among some parties. Empirical data can contain information about causation rather than mere correlation. Here Chaves et al. present an algorithm for computing constraints on the correlations arising from a given quantum causal structure, and apply this framework to the information causality principle and networked architectures.