Related papers: Topological Contextuality and Quantum Representati…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level.…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer…
Contextuality is considered as an intrinsic signature of non-classicality, and a crucial resource for achieving unique advantages of quantum information processing. However, recently there have been debates on whether classical fields may…
Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality--the denial of a notion of classical physical…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…
Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open. First, determining the complexity of deciding if…
Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…