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Non-Kolmogorovian Probabilities and Quantum Technologies.

Federico Hernán Holik¹

¹Instituto de Física La Plata, CONICET-UNLP, Diagonal 113 e/63 y 64, La Plata 1900, Argentina.

Entropy (Basel, Switzerland)

|November 24, 2022

Summary

This study explores the philosophical and technical challenges of non-Kolmogorovian probability, linking it to quantum contextuality and potential quantum computing speed-ups. We use this framework to conceptually analyze quantum theory problems.

Keywords:

non-Kolmogorovian probability philosophy of quantum physics quantum technologies

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Area of Science:

Foundations of Quantum Mechanics
Probability Theory
Quantum Information Science

Background:

Quantum contextuality is a key feature of quantum theory, potentially linked to quantum computing advantages.
The axiomatization of non-Kolmogorovian probability presents significant philosophical and technical challenges.
Existing research primarily focuses on the physics aspects, leaving philosophical questions underexplored.

Purpose of the Study:

To investigate the philosophical underpinnings of non-Kolmogorovian probability.
To explore the technical challenges in axiomatizing this probability framework.
To connect the non-Kolmogorovian approach to the problem of quantum contextuality and its implications.

Main Methods:

Conceptual analysis of foundational issues in quantum probability.
Application of the non-Kolmogorovian probability framework as a technical tool.
Examination of the relationship between quantum contextuality and probability axiomatization.

Main Results:

Identified key philosophical questions surrounding non-Kolmogorovian probability.
Demonstrated the utility of the non-Kolmogorovian approach for analyzing quantum contextuality.
Highlighted the technical difficulties in formally axiomatizing the non-Kolmogorovian framework.

Conclusions:

The non-Kolmogorovian probability framework offers valuable insights into quantum contextuality.
Further philosophical and technical work is needed to fully axiomatize non-Kolmogorovian probability.
Understanding quantum contextuality may require moving beyond standard Kolmogorovian probability.