The three types of normal sequential effect algebras

  title={The three types of normal sequential effect algebras},
  author={Abraham Westerbaan and Bas Westerbaan and John van de Wetering},
A sequential effect algebra (SEA) is an effect algebra equipped with a sequential product operation modeled after the Lüders product (a,b)↦aba on C∗-algebras. A SEA is called normal when it has all suprema of directed sets, and the sequential product interacts suitably with these suprema. The effects on a Hilbert space and the unit interval of a von Neumann or JBW algebra are examples of normal SEAs that are in addition convex, i.e. possess a suitable action of the real unit interval on the… 
A computer scientist's reconstruction of quantum theory
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order
A Categorical Construction of the Real Unit Interval
The real unit interval is the fundamental building block for many branches of mathematics like probability theory, measure theory, convex sets and homotopy theory. However, a priori the unit interval
Quantum Theory from Principles, Quantum Software from Diagrams
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning,
A characterisation of ordered abstract probabilities
A structure theory for effect monoids that are ω-complete, i.e. where every increasing sequence has a supremum is presented, which gives an algebraic characterisation and motivation for why any physical or logical theory would represent probabilities by real numbers.


Sequential products on effect algebras
Three characterisations of the sequential product
It has already been established that the properties required of an abstract sequential product as introduced by Gudder and Greechie are not enough to characterise the standard sequential product
Blocks of homogeneous effect algebras
  • Gejza Jenvca
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2001
Effect algebras, introduced by Foulis and Bennett in 1994, are partial algebras which generalise some well known classes of algebraic structures (for example orthomodular lattices, MV algebras,
Open Problems for Sequential Effect Algebras
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with certain natural properties is defined. In such structures, we can study combinations of simple measurements
Type-Decomposition of an Effect Algebra
Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets,
Sequential product on standard effect algebra {\cal E} (H)
This paper characterize some algebraic properties of the abstract sequential product of a quantum effect A on a complex Hilbert space H and presents a general method for constructing sequential products on and studies some property of the sequential products constructed by the method.
An Introduction to Effectus Theory
This text is an account of the basics of effectus theory, which includes the fundamental duality between states and effects, with the associated Born rule for validity of an effect (predicate) in a particular state.
Sequential product on effect logics
In categorical logic predicates on an object X are traditionally represented as subobjects. Jacobs proposes [9] an alternative in which the predicates on X are maps p : X → X + X with [id, id] ◦ p =
Tensor Product of Distributive Sequential Effect Algebras and Product Effect Algebras
Abstract A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural properties is defined. We define the tensor product of two