Measure-theoretic approach to negative probabilities

TL;DR

This paper introduces a measure-theoretic framework for negative probabilities, explores a contextuality measure, and applies it to quantum physics and quantum computing, revealing insights into the role of contextuality.

Contribution

It develops a measure-theoretic approach to negative probabilities and characterizes a new contextuality measure with applications in quantum physics and quantum computing.

Findings

The contextuality measure has well-defined properties.

Negative probabilities can be analyzed using measure theory.

Contextuality plays a significant role in quantum computing circuits.

Abstract

In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum physics. In particular, we study the role played by contextuality in quantum computing circuits.