# 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} }

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

- MathematicsQuantum
- 2019

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

- Computer ScienceFoundations 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

### Convex and Sequential Effect Algebras

- Mathematics
- 2018

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

- Mathematics
- 2018

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

- Mathematics
- 2001

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

- Mathematics
- 2003

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

- Mathematics, Computer Science
- 1999

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

- Mathematics
- 1994

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

- Mathematics
- 2011

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

- Physics
- 2010

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

- Mathematics
- 1998

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…