Contexts in Convex and Sequential Effect Algebras

@article{Gudder2019ContextsIC,
  title={Contexts in Convex and Sequential Effect Algebras},
  author={Stanley P. Gudder},
  journal={Electronic Proceedings in Theoretical Computer Science},
  year={2019}
}
  • S. Gudder
  • Published 30 January 2019
  • Mathematics
  • Electronic Proceedings in Theoretical Computer Science
A convex sequential effect algebra (COSEA) is an algebraic system with three physically motivated operations, an orthogonal sum, a scalar product and a sequential product. The elements of a COSEA correspond to yes-no measurements and are called effects. In this work we stress the importance of contexts in a COSEA. A context is a finest sharp measurement and an effect will act differently according to the underlying context with which it is measured. Under a change of context, the possible… 
3 Citations

On the properties of spectral effect algebras

The aim of this paper is to show that there can be either only one or uncountably many contexts in any spectral effect algebra, answering a question posed in [S. Gudder, Convex and Sequential Effect

Contexts in Quantum Measurement Theory

  • S. Gudder
  • Computer Science
    Foundations of Physics
  • 2019
This work considers properties of channels and contexts, and shows that the set of sharp channels can be given a natural partial order in which contexts are the smallest elements.

References

SHOWING 1-10 OF 23 REFERENCES

Sequential products on effect algebras

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

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

Sequential quantum measurements

A quantum effect is an operator A on a complex Hilbert space H that satisfies 0⩽A⩽I. We denote the set of quantum effects by E(H). The set of self-adjoint projection operators on H corresponds to

Sequential product of quantum effects

Unsharp quantum measurements can be modelled by means of the class e(H) of positive contractions on a Hilbert space H, in brief, quantum effects. For A, B ∈ e(H) the operation of sequential product

Convex Structures and Effect Algebras

This work shows that any convex effectalgebra admits a representation as a generating initialinterval of an ordered linear space,alogous to a classical representation theorem for convex structures due to M. H. Stone.

Effect algebras and unsharp quantum logics

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among

The sheaf-theoretic structure of non-locality and contextuality

It is shown that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections, and a linear algebraic approach to computing these obstructions is described, which allows a systematic treatment of arguments for non- Locality and contextuality.

Deep Beauty: A Universe of Processes and Some of Its Guises

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual

Sharp and Unsharp Quantum Effects

A survey of the algebraic and the statistical properties of sharp and unsharp quantum effects is presented. We begin with a discussion and a comparison of four types of probability theories, the