Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, resource theories also make it possible to recast these already established theories on a new language, providing not only new perspectives on the potential of physical phenomena as valuable resources for technological development, for example, but they also provide insights into the very foundations of these theories. In this work, we will investigate some properties of a resource theory for quantum contextuality, an essential characteristic of quantum phenomena that ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made. We will present the resource theory to be studied and investigate certain global properties of this theory using tools and methods that, although already developed and studied by the community in other resource theories, had not yet been used to characterize resource theories of contextuality. In particular, we will use the so called cost and yield monotones, making use of their power in the study of resource theories for nonlocality, in an attempt to extend these results to this more general class of phenomena, contextuality.
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, resource theories also make it possible to recast these already established theories on a new language, providing not only new perspectives on the potential of physical phenomena as valuable resources for technological development, for example, but they also provide insights into the very foundations of these theories. In this work, we will investigate some properties of a resource theory for quantum contextuality, an essential characteristic of quantum phenomena that ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made. We will present the resource theory to be studied and investigate certain global properties of this theory using tools and methods that, although already developed and studied by the community in other resource theories, had not yet been used to characterize resource theories of contextuality. In particular, we will use the so called cost and yield monotones, making use of their power in the study of resource theories for nonlocality, in an attempt to extend these results to this more general class of phenomena, contextuality.
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes.For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, resource theories also make it possible to recast these already established theories on a new language, providing not only new perspectives on the potential of physical phenomena as valuable resources for technological development, for example, but they also provide insights into the very foundations of these theories.In this work, we will investigate some properties of a resource theory for quantum contextuality, an essential characteristic of quantum phenomena that ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made.We will present the resource theory to be studied and investigate certain global properties of this theory using tools and methods that, although already developed and studied by the community in other resource theories, had not yet been used to characterize resource theories of contextuality.In particular, we will use the so called cost and yield monotones, making use of their power in the study of resource theories for nonlocality, in an attempt to extend these results to this more general class of phenomena, contextuality.
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, resource theories also make it possible to recast these already established theories on a new language, providing not only new perspectives on the potential of physical phenomena as valuable resources for technological development, for example, but they also provide insights into the very foundations of these theories. In this work, we will investigate some properties of a resource theory for quantum contextuality, an essential characteristic of quantum phenomena that ensures the impossibility of interpreting the results of quantum measurements as revealing properties that are independent of the set of measurements being made. We will present the resource theory to be studied and investigate certain global properties of this theory using tools and methods that, although already developed and studied by the community in other resource theories, had not yet been used to characterize resource theories of contextuality. In particular, we will use the so called cost and yield monotones, extending the results of reference Quantum 4, 280 (2020) to general contextuality scenarios.
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrization. Then, using an efficient linear programming characterization for the noncontextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocality to obtain natural monotones for generalized contextuality in arbitrary prepare-and-measure experiments.
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.
How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act on physical systems. This approach has advanced our understanding of fundamental physical principles, such as the second law of thermodynamics, and provided operational measures to quantify resources such as entanglement or information content. In this work, we significantly extend the approach and range of applicability of resource theories. Firstly we generalize the notion of resource theories to include any description or knowledge that agents may have of a physical state, beyond the density operator formalism. We show how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed. The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.
We aim to counter the tendency for specialization in science by advancing a language that can facilitate the translation of ideas and methods between disparate contexts. The focus is on questions of "resource-theoretic nature". In a resource theory, one identifies resources and allowed manipulations that can be used to transform them. Some of the main questions are: How to optimize resources? What are the trade-offs between them? Can a given resource be converted to another one via the allowed manipulations? Because of their ubiquity, methods used to answer them in one context can be used to tackle corresponding questions in new contexts. The translation occurs in two stages. Firstly, methods are generalized to the abstract language. Then, one can determine whether potentially novel contexts can accommodate them. We focus on the first stage, by introducing two variants of an abstract framework in which existing and yet unidentified resource theories can be represented. Using these, the task of generalizing concrete methods is tackled in chapter 4 by studying the ways in which meaningful measures of resources may be constructed. One construction expresses a notion of cost (or yield) of a resource. Among other applications, it may be used to extend measures from a subset of resources to a larger domain. Another construction allows the translation of resource measures from one resource theory to another. Special cases include resource robustness and weight measures, as well as relative entropy based measures quantifying minimal distinguishability from freely available resources. We instantiate some of these ideas in a resource theory of distinguishability in chapter 5. It describes the utility of systems with probabilistic behavior for the task of distinguishing between hypotheses, which said behavior may depend on.