Related papers: Contexts in Convex and Sequential Effect Algebras
We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a…
We first show that the convex effect algebras (CEA) approach to quantum mechanics is more general than the general probabilistic theories approach. We then restrict our attention to finite-dimension CEA's. After an introductory Section~1,…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
A sequential effect algebra (SEA) is an effect algebra equipped with a sequential product operation modeled after the L\"uders product $(a,b)\mapsto \sqrt{a}b\sqrt{a}$ on C*-algebras. A SEA is called normal when it has all suprema of…
A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential…
This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and possess an order-determining set of states. We then discuss…
This paper studies convex sets categorically, namely as algebras of a distribution monad. It is shown that convex sets occur in two dual adjunctions, namely one with preframes via the Boolean truth values {0,1} as dualising object, and one…
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…
Our basic concept is the set $\mathcal{E}(H)$ of effects on a finite dimensional complex Hilbert space $H$. If $a,b\in\mathcal{E}(H)$, we define the sequential product $a[\mathcal{I}]b$ of $a$ then $b$. The sequential product depends on the…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
Mixed-effects models are fundamental tools for analyzing clustered and repeated-measures data, but existing high-dimensional methods largely focus on penalized estimation with vector-valued covariates. Bayesian alternatives in this regime…
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…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
Semantic code search, which aims to retrieve code snippets relevant to a given natural language query, has attracted many research efforts with the purpose of accelerating software development. The huge amount of online publicly available…
Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of…