Related papers: Contexts in Convex and Sequential Effect Algebras
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
Humans effortlessly identify objects by leveraging a rich understanding of the surrounding scene, including spatial relationships, material properties, and the co-occurrence of other objects. In contrast, most computational object…
Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in…
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the…
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their…
Quantum contextuality is a concept used to describe the property of hidden-variable theory that measurement outcomes predetermined by the hidden variables depend on the measurement context. The term measurement context can have different…
Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…
Opial's Lemma is a fundamental result in the convergence analysis of sequences generated by optimization algorithms in real Hilbert spaces. We introduce the concept of Opial sequences - sequences for which the limit of the distance to each…
Warning: This paper contains content that may be offensive or upsetting. Understanding the harms and offensiveness of statements requires reasoning about the social and situational context in which statements are made. For example, the…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, when understood as a resource for quantum…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
We reframe the EPR argument through an operational lens, replacing the notion of fixed "elements of reality" with context-indexed conditional states - what's often referred to as a measurement assemblage. This move deliberately sidesteps…
Structural Equation Modeling (SEM) or Covariance Structure Analysis (CSA) is a versatile and powerful method in the social and behavioral sciences, providing a framework for modeling complex relationships, testing mediation, accounting for…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…