# Representation of Super-Quantum probability

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• DarMM
In summary, classical probability theory is based on measure spaces and functions, while quantum probability is based on Hilbert spaces and operators. Both of these concepts are abstractly described using the theory of C*-algebras and their duals. However, there is currently no known mathematical structure for Super-Quantum Correlations that exceed Tsirelson's bound, such as those found in PR boxes. While these correlations have been presented as a matrix of probabilities attached to events, there is still no general mathematical theory for them. The question remains if such a theory exists, as posed in a related paper.
DarMM
Gold Member
Classical probability theory can be represented with measure spaces and functions over them. Quantum Probability is given as the theory of Hilbert spaces and operators over them. Both more abstractly are handled by the theory of C*-algebras and their duals.

However I know of no structure for Super-Quantum Correlations violating Tsirelson's bound, such as those found in PR boxes. I've always seen them presented merely as a matrix of probabilities attached to events, but never seen a general mathematical theory. I was just wondering if there is one?

## What is "Representation of Super-Quantum probability"?

"Representation of Super-Quantum probability" refers to the mathematical and conceptual framework used to describe and analyze probabilities in systems that go beyond the traditional quantum realm. These systems are characterized by non-locality, non-commutativity, and non-associativity, and require a different approach to understanding probabilities.

## How is Super-Quantum probability different from traditional quantum probability?

Super-Quantum probability is different from traditional quantum probability in that it extends beyond the limitations of quantum mechanics. While traditional quantum probability deals with probabilities in systems that are local, commutative, and associative, Super-Quantum probability takes into account systems that exhibit non-locality, non-commutativity, and non-associativity.

## What are the applications of Super-Quantum probability?

Super-Quantum probability has potential applications in various fields, including quantum computing, cryptography, and information theory. It can also be used to study complex systems in physics, biology, and social sciences, where traditional quantum mechanics may not be sufficient.

## What are the challenges in representing Super-Quantum probability?

One of the main challenges in representing Super-Quantum probability is finding a suitable mathematical framework that can accurately describe and analyze probabilities in these systems. Another challenge is understanding the implications and consequences of non-locality, non-commutativity, and non-associativity in these systems.

## What are some current research trends in Super-Quantum probability?

Current research in Super-Quantum probability is focused on developing new mathematical tools and techniques to represent and analyze probabilities in these systems. There is also ongoing research on the potential applications of Super-Quantum probability in various fields and the implications of non-locality, non-commutativity, and non-associativity in these systems.

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