In this chapter, we will discuss the ontological status of the notion of quantuminformation. In the first part, we review the mathematical framework ofa generalized information theory. In this framework, probability theory will play a central role and, thus, we will devote Section 2 to it.We argue that the existence of probabilistic models that go beyond the classical and quantum realms, and the possibility of performing informational protocols in those models, allow us to claim that a generalized information theory can be conceived. Notice that this perspective is complementary to that of other research programs (see, e.g., Holik et al. 2015; Holik et al. 2016, and references therein). In the second part, we will consider the question about the ontology of the possible models satisfying the different instances of that generalized formalism. This will be the content of Section 3. Specifically, we want to study the role quantum mechanics plays in quantum information protocols; the question is whether there are other possible ontologies that can perform the same tasks. We will relate this problem to the existence of many examples of physical systems that are actually constructed using an essentially classical ontology but, on the other hand, are modeled by structures resembling the laws of quantum mechanics (e.g. Aerts 1998; Kwiat et al. 2000; Spreeuw 2001;Couder et al. 2005; Couder and Fort 2006; Qian et al. 2015). Their significancefor us relies in the fact that they can be used to perform quantum information protocols (though, in an inefficient way) (Man?ko et al. 2001; Bhattacharya et al. 2002; Francisco et al. 2006a, 2006b; Francisco and Ledesma 2008; Goldin et al. 2010). On this basis, we will explore the ontological implications of the existence of these simulations. Finally, in Section 4 we will draw our conclusions.
In this chapter, we will discuss the ontological status of the notion of quantuminformation. In the first part, we review the mathematical framework ofa generalized information theory. In this framework, probability theory will play a central role and, thus, we will devote Section 2 to it.We argue that the existence of probabilistic models that go beyond the classical and quantum realms, and the possibility of performing informational protocols in those models, allow us to claim that a generalized information theory can be conceived. Notice that this perspective is complementary to that of other research programs (see, e.g., Holik et al. 2015; Holik et al. 2016, and references therein). In the second part, we will consider the question about the ontology of the possible models satisfying the different instances of that generalized formalism. This will be the content of Section 3. Specifically, we want to study the role quantum mechanics plays in quantum information protocols; the question is whether there are other possible ontologies that can perform the same tasks. We will relate this problem to the existence of many examples of physical systems that are actually constructed using an essentially classical ontology but, on the other hand, are modeled by structures resembling the laws of quantum mechanics (e.g. Aerts 1998; Kwiat et al. 2000; Spreeuw 2001;Couder et al. 2005; Couder and Fort 2006; Qian et al. 2015). Their significancefor us relies in the fact that they can be used to perform quantum information protocols (though, in an inefficient way) (Man?ko et al. 2001; Bhattacharya et al. 2002; Francisco et al. 2006a, 2006b; Francisco and Ledesma 2008; Goldin et al. 2010). On this basis, we will explore the ontological implications of the existence of these simulations. Finally, in Section 4 we will draw our conclusions.
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 article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic framework for the formulation of mathematical models of physical systems that is general enough to encompass classical and quantum mechanical models. After a short discussion on the properties of classical systems (realism and determinism), we move on to the study of a general class of quantum-mechanical models of physical systems and explain what some of the key problems in a quantum theory of observations and measurements are. In the last part of our essay, we attempt to elucidate the roles played by entanglement between a system and its environment and of information loss in understanding "decoherence" and "dephasing", which are key mechanisms in a quantum theory of measurements and experiments. We also discuss the problem of "time in quantum mechanics" and sketch an answer to the question when an experiment can be considered to have been completed successfully.
This thesis investigates three distinct facets of the theory of quantum information. The first two, quantum state estimation and quantum process estimation, are closely related and deal with the question of how to estimate the classical parameters in a quantum mechanical model. The third attempts to bring quantum theory as close as possible to classical theory through the formalism of quasi-probability. \n \nBuilding a large scale quantum information processor is a significant challenge. First, we require an accurate characterization of the dynamics experienced by the device to allow for the application of error correcting codes and other tools for implementing useful quantum algorithms. The necessary scaling of computational resources needed to characterize a quantum system as a function of the number of subsystems is by now a well studied problem (the scaling is generally exponential). However, irrespective of the computational resources necessary to just write-down a classical description of a quantum state, we can ask about the experimental resources necessary to obtain data (measurement complexity) and the computational resources necessary to generate such a characterization (estimation complexity). These problems are studied here and approached from two directions. \n \nThe first problem we address is that of quantum state estimation. We apply high-level decision theoretic principles (applied in classical problems such as, for example, universal data compression) to the estimation of a qubit state. We prove that quantum states are more difficult to estimate than their classical counterparts by finding optimal estimation strategies. These strategies, requiring the solution to a difficult optimization problem, are difficult to implement in practise. Fortunately, we find estimation algorithms which come close to optimal but require far fewer resources to compute. Finally, we provide a classical analog of this quantum mechanical problem which reproduces, and gives intuitive explanations for, many of its features, such as why adaptive tomography can quadratically reduce its difficulty. \n \nThe second method for practical characterization of quantum devices takes is applied to the problem of quantum process estimation. This differs from the above analysis in two ways: (1) we apply strong restrictions on knowledge of various estimation and control parameters (the former making the problem easier, the latter making it harder); and (2) we consider the problem of designing future experiments based on the outcomes of past experiments. We show in test cases that adaptive protocols can exponentially outperform their off-line counterparts. Moreover, we adapt machine learning algorithms to the problem which bring these experimental design methodologies to realm of experimental feasibility. \n \nIn the final chapter we move away from estimation problems to show formally that a classical representation of quantum theory is not tenable. This intuitive conclusion is formally borne out through the connection to quasi-probability -- where it is equivalent to the necessity of negative probability in all such representations of quantum theory. In particular, we generalize previous no-go theorems to arbitrary classical representations of quantum systems of arbitrary dimension. We also discuss recent progress in the program to identify quantum resources for subtheories of quantum theory and operational restrictions motivated by quantum computation.
Introduction Quantum information theory is the study of how the peculiar features of quantum mechanics can be exploited for the purposes of information processing and transmission. A central theme of such a study is the ways in which quantum mechanics opens up possibilities that go beyond what can be achieved classically. This has in turn led to a renewed interest in, and a new perspective on, the differences between the classical and the quantum. Although much of the work along these lines has been motivated by quantum information theory – and some of it has been motivated by the conviction that quantum theory is essentially about possibilities of information processing and transmission – the results obtained, and the frameworks developed, have interest even for those of us who are not of that conviction. Indeed, much of the recent work echoes, and builds upon, work that predates the inception of quantum information theory. The significance of such work extends beyond the setting of quantum information theory; the work done on distinguishing the quantum from the classical in the context of frameworks that embrace both is something worthy of the attention of anyone interested in the foundational issues surrounding quantum theory. One of the striking features of quantum mechanics lies in its probabilistic character. A quantum state yields, not a definite prediction of the outcome of an experiment, but a probability measure on the space of possible outcomes. Of course, probabilities occur also in a classical context.
Short Description This paper investigates whether the relational turn in quantum theory and category-theoretic physics is sufficient to constitute a genuinely generative ontology. It distinguishes state change, probabilistic actualization, and compositional generation from the stronger transformation of the possibility architecture itself. The paper proposes Generative-Resonant Ontology, E = Phi R, organized by the recursive cycle Phi_t -> R_t -> S_t -> Phi_(t+1), in which actuality may participate in changing what can become possible next. Extended Description Modern physics has progressively displaced the classical image of reality as a collection of independently determined states. Classical mechanics formalized physical existence through states and trajectories; quantum mechanics placed structured possibility at the center of physical description; Relational Quantum Mechanics made physical values dependent upon interactions between systems; and categorical approaches to quantum theory foregrounded morphisms, processes, and composition. These developments constitute a profound movement from substance-centered toward relational and process-centered ontology. This paper argues, however, that relationality is not yet equivalent to generativity. A theory may describe relational actualization, compositional novelty, particle creation, or even highly complex emergent organization while still operating within a sufficiently pre-specified architecture of admissible states, entities, relations, and transformations. To make this distinction precise, the paper differentiates four meanings of generation: State change:S_t -> S_(t+1) Actualization of prior possibility:Phi_given -> R -> S Compositional generation:f, g -> g o f Possibility-space generation:Phi_t -> R_t -> S_t -> Phi_(t+1) The first three are classified as Weak Generativity, whereas Strong Generativity occurs when relationally constituted actuality participates in transforming the effective structure of subsequent possibility. This distinction motivates Generative-Resonant Ontology: E = Phi R expressed recursively as: Phi_t -> R_t -> S_t -> Phi_(t+1) Here, Phi is not a Hilbert space, wave function, probability distribution, or collection of possible states. It denotes structured, historically transformable openness. R denotes relational participation, and S denotes provisional crystallization. The decisive innovation is the final transition: S_t -> Phi_(t+1) Actuality is therefore not merely the endpoint of possibility actualization but may become an enabling condition for a transformed future possibility regime. The paper tests this distinction against quantum field theory, particle creation, phase transitions, spontaneous symmetry breaking, quasiparticles, and emergence. It distinguishes epistemic, descriptive, and ontological novelty and argues that emergent effective regimes constitute the strongest current candidates for strong generativity at the effective level, while avoiding the stronger claim that fundamental physical possibility spaces are known to evolve. Finally, the paper formulates a mathematical research program centered on: Omega_t --(R_t, S_t)--> Omega_(t+1) and, categorically: C_t -> C_(t+1) while recognizing the meta-rule problem that arises when the rule governing structural change is itself pre-specified. The resulting proposal is an ontological extension of the relational turn rather than a replacement for quantum theory. The central question is no longer merely which possibility becomes actual, but how actuality may transform what can become possible next. Highlights Distinguishes Relationality from Generativity. Introduces four meanings of generation:State Change, Actualization, Composition, and Possibility-Space Generation. Defines the first three as Weak Generativity and the fourth as Strong Generativity. Establishes the central distinction: Quantum Uncertainty != Generative Openness Proposes Generative-Resonant Ontology: E = Phi R Introduces the recursive structure: Phi_t -> R_t -> S_t -> Phi_(t+1) Identifies: S -> Phi' as the decisive transition from relational actualization to generative reopening. Distinguishes Epistemic Novelty, Descriptive Novelty, and Ontological Novelty. Treats phase transitions, spontaneous symmetry breaking, and emergent effective degrees of freedom as a boundary zone toward strong effective generativity. Replaces the simple opposition between closed and open systems with: Pre-Specified Relational SpaceversusSelf-Transforming Possibility Space Formulates a future mathematical research program around: Omega_t --(R_t, S_t)--> Omega_(t+1) and: C_t -> C_(t+1) Explicitly distinguishes physical formalism from ontological interpretation. Brief Summary of Each Part Part I. Framing the Problem: Is Quantum Theory Truly a Theory of Generation?Establishes the central problem of the paper. The transition from classical states to quantum possibility, relational events, and categorical processes does not automatically establish strong generativity. The key issue is whether relation merely actualizes possibility or can generate the structure of future possibility. Part II. Classical Physics: Existence as StateReconstructs classical physics as a state-centered ontology in which: S_t -> S_(t+1) occurs within a sufficiently specified state space Omega. The central distinction is between movement through possibility and transformation of the possibility architecture itself. Part III. Quantum Mechanics: From State to Possibility and RelationShows how superposition, measurement, interaction, and entanglement move physical ontology beyond classical determinate states toward structured possibility and relational actualization. The basic heuristic structure is: Phi_given -> R -> S while quantum possibility is distinguished from generative Phi. Part IV. Relational Quantum Mechanics: The Ontologization of RExamines RQM as a major ontological shift from relations between already determinate facts toward relations as constitutive of physical facts. It identifies the first generativity gap: R -> S does not imply S -> Phi' Part V. Categorical Quantum Mechanics: From Objects to Processes and CompositionAnalyzes the categorical move from objects toward morphisms, processes, and composition: f, g -> g o f It identifies the second generativity gap: Compositional novelty does not imply generation of relational grammar. Part VI. Refining the Meaning of “Closure”Rejects a simple characterization of category theory as “closed.” It introduces the distinction between Pre-Specified Relational Space and Self-Transforming Possibility Space and separates operational openness from generative openness. Part VII. Four Meanings of GenerationDistinguishes: State ChangeS_t -> S_(t+1) ActualizationPhi_given -> R -> S Compositionf, g -> g o f Possibility-Space GenerationPhi_t -> R_t -> S_t -> Phi_(t+1) The first three constitute Weak Generativity; the fourth constitutes Strong Generativity. Part VIII. Quantum Field Theory, Emergence, and Phase Transitions as CounterargumentsTests the distinction against particle creation, spontaneous symmetry breaking, phase transitions, and emergent degrees of freedom. It distinguishes: 0 -> 1 -> 2 from: Omega_t -> Omega_(t+1) and treats emergence as a serious boundary case. Part IX. Is Emergence Phi'?Distinguishes Epistemic Novelty, Descriptive Novelty, and Ontological Novelty. Emergence qualifies as a candidate for Phi' when newly stabilized structures transform what can subsequently exist, relate, or become dynamically accessible. Part X. Generative-Resonant OntologyPresents the theory fully through: E = Phi R and: Phi_t -> R_t -> S_t -> Phi_(t+1) S is reinterpreted as provisional crystallization rather than final actuality. Part XI. Phi and Quantum Possibility: Why Generative Openness Is Not Quantum UncertaintyEstablishes that: Phi != {S_1, S_2, ..., S_n} Phi != H Phi != |psi> Phi != P(S) Phi != Quantum Uncertainty The key distinction is between: “Which possibility becomes actual?” and: “What becomes possible because this actuality occurred?” Part XII. How Can Possibility Space Itself Be Formalized?Converts the ontology into a mathematical research program: Omega_t --(R_t, S_t)--> Omega_(t+1) and: C_t -> C_(t+1) It also identifies the meta-rule problem: if a transformation rule is itself entirely pre-specified, generativity may merely have been displaced to a higher formal level. Part XIII. The Boundary Between Physical Claims and Ontological ClaimsClarifies that Generative-Resonant Ontology does not modify quantum mechanics or claim new quantum predictions. Its current status is an ontological interpretation and formal research hypothesis constrained by, but not entailed by, existing physics. Part XIV. An Integrated Model: Three Ontological Stages in the Development of Physical ThoughtIntegrates the paper into three conceptual stages: Being as State:S_t -> S_(t+1) Being as Relational Actualization:Phi_given -> R -> S Being as Generative Reopening:Phi_t -> R_t -> S_t -> Phi_(t+1) These are treated as nested ontological expansions rather than simple historical replacements. Part XV. Conclusion: From a Relational World to a Generative WorldConcludes with the transition: R -> S to: R -> S -> Phi' and ultimately: Phi -> R -> S -> Phi' Reality is interpreted as a history in which relationally constituted actuality may participate in transforming the horizon of future possibility. Academic Contributions 1. Distinguishing Relationality from Generativity The paper introduces the fundamental distinction: Relationality != Generativity Relationality concerns how actuality depends upon or is constituted through relations. Generativity concerns whether relational actuality transforms the structure of subsequent possibility. 2. A Fourfold Taxonomy of Generation The paper distinguishes: State Ch