I introduce an algorithm to detect one-way quantum information between two interacting quantum systems, i.e. the direction and orientation of the information transfer in arbitrary quantum dynamics. I then build an information-theoretic quantifier of one-way information which satisfies a set of desirable axioms. In particular, it correctly evaluates whether correlation implies one-way quantum information, and when the latter is transferred between uncorrelated systems. In the classical scenario, the quantity measures information transfer between random variables. I also generalize the method to identify and rank concurrent sources of quantum information flow in many-body dynamics, enabling to reconstruct causal patterns in complex networks.
I introduce an algorithm to detect one-way quantum information between two interacting quantum systems, i.e. the direction and orientation of the information transfer in arbitrary quantum dynamics. I then build an information-theoretic quantifier of one-way information which satisfies a set of desirable axioms. In particular, it correctly evaluates whether correlation implies one-way quantum information, and when the latter is transferred between uncorrelated systems. In the classical scenario, the quantity measures information transfer between random variables. I also generalize the method to identify and rank concurrent sources of quantum information flow in many-body dynamics, enabling to reconstruct causal patterns in complex networks.
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.
We present a framework for quantifying information flow within general quantum processes. For this purpose, we introduce the signaling power of quantum channels and discuss its relevant operational properties. This function supports extensions to higher-order maps, enabling the evaluation of information flow in general quantum causal networks and processes with indefinite causal order. Furthermore, our results offer a rigorous approach to information dynamics in open systems that applies also in the presence of initial system-environment correlations, and allows for the distinction between classical and quantum information backflow.
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.
Information integration measures quantify coordination in complex systems, but conflate correlation with causation. High mutual information can arise from genuine causal influence, common inputs, or independent dynamics with shared constraints. We introduce a theoretical framework distinguishing these mechanisms through causal efficiency ρ=TE/MI, the fraction of correlation reflecting genuine information flow rather than self-prediction. We prove that this framework is mathematically equivalent to standard integration measures under bounded distortion, with distortion constants revealing three distinct regimes: (I) high causality where correlation accurately reflects integration, (II) heterogeneous coupling where structure matters, and (III) low causal efficiency where correlation masquerades as coordination. Applied to quantum measurement, we show that the triadic coordination capacity framework (duration, frequency, agency) provides natural context for detecting regime transitions. The formalism makes testable predictions: coordination events should exhibit ρ>0.7 during genuine integration, while decoherence shows ρ<0.3 despite persistent correlation. This establishes rigorous causal foundations for integration theory and characterizes when correlation-based measures succeed or systematically fail.
Within the framework of Information Theory, the existence of correlations between two random variables means that we can obtain information about one of them, just by measuring or observing the other random variable. In certain cases, this kind of relationship allows obtaining information about a variable even when the other is separated by a very large distance, that is, the process of obtaining information is non-local, an example (if not the only) is the quantum entanglement. These features of correlations make it interesting and important to study, classify and quantify them. The correlations are classified into classical correlations and quantum correlations, in addition they are quantified through the mutual information. Here we will present a natural way to define classical mutual information and then we will generalize it to the quantum case. Furthermore, every term in the definitions of mutual information will be interpreted using the concepts of classical and quantum entropy.
Communication complexity, which quantifies the minimum communication required for distributed computation, offers a natural setting for investigating the capabilities and limitations of quantum mechanics in information processing. We introduce an information-theoretic approach to study one-way communication complexity based solely on the axioms of mutual information. Within this framework, we derive an extended statement of the information causality principle, which recovers known lower bounds on the communication complexities for a range of functions in a simplified manner and leads to new results. We further prove that the extended information causality principle is at least as strong as the principle of non-trivial communication complexity in bounding the strength of quantum correlations attainable in Bell experiments. Our study establishes a new route for exploring the fundamental limits of quantum technologies from an information-theoretic viewpoint.