Quantum Probability and The Foundations of Quantum Theory

M. D. Srinivas

Jürg Martin Fröhlich, Baptiste Schubnel

Jincheng Zhang

Probability Information Theory (PIT) is a foundational branch of theoretical computer science concerned with the mathematical properties of probability and its relationship to computation. This paper investigates the convergence of PIT with quantum computing, specifically exploring the nature and application of probability information within quantum algorithms. We propose a novel framework where PIT's theoretical foundations are integrated with quantum algorithm design, leveraging PIT's inherent strengths to guide and optimize quantum computations. This investigation aims to uncover potential new applications of quantum algorithms based on the unique properties of probability information, pushing the boundaries of computational exploration.

Luigi Accardi

This conference was devoted to fundamental questions raised by quantum mechanics, especially in quantum information theory. As has become customary in our series of conference in Vaxjo, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the foundations of probability and physics. This conference belongs to the series of Vaxjo conferences in foundations of quantum mechanics (especially probabilistic foundations) combined of two subseries, Foundations of Probability and Physics: 2000, 02, 04, 06, 08, and Quantum Theory: Reconsideration of Foundations: 2001, 03, 05, 07. We also mention the first Vaxjo conference: Bohmian mechanics 2000. This is definitely the longest series of conferences on foundations in the history of quantum mechanics.

Stanley Gudder

Mike Oaksford

This comment suggests that Pothos & Busmeyer (P&B) do not provide an intuitive rational foundation for quantum probability (QP) theory to parallel standard logic and classical probability (CP) theory. In particular, the intuitive foundation for standard logic, which underpins CP, is the elimination of contradictions - that is, believing p and not-p is bad. Quantum logic, which underpins QP, explicitly denies non-contradiction, which seems deeply counterintuitive for the macroscopic world about which people must reason. I propose a possible resolution in situation theory.