# Sequences of projective measurements in generalized probabilistic models

@article{Kleinmann2014SequencesOP, title={Sequences of projective measurements in generalized probabilistic models}, author={Matthias Kleinmann}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2014}, volume={47} }

We define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the hypothetical Popescu–Rohrlich box. For quantum mechanics, the definition yields the established Lüders rule, which is the standard rule for updating the quantum state after a measurement. For the general case, it can be seen as being the least disturbing or…

## 19 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

Information processing in generalized probabilistic theories

- Physics
- 2005

A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.

Typical local measurements in generalized probabilistic theories: emergence of quantum bipartite correlations.

- PhysicsPhysical review letters
- 2013

It is found that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics.

Quantum mechanics as quantum measure theory

- Physics
- 1994

The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields…

Conditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics

- Mathematics
- 2012

Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including
classical…

State-independent experimental test of quantum contextuality

- PhysicsNature
- 2009

The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical…

Three Slit Experiments and the Structure of Quantum Theory

- Physics
- 2011

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an…

Information Processing in Convex Operational Theories

- PhysicsElectron. Notes Theor. Comput. Sci.
- 2011

Quantum measuring processes of continuous observables

- Mathematics
- 1984

The purpose of this paper is to provide a basis of theory of measurements of continuous observables. We generalize von Neumann’s description of measuring processes of discrete quantum observables in…

Generalizations of Boxworld

- Physics
- 2012

Boxworld is a toy theory that can generate extremal nonlocal correlations known as PR boxes. These have been well established as an important tool to examine general nonlocal correlations, even…