Quantum Probability for Probabilists

Federico Holik, César Massri, Angelo Plastino +1 more

We discuss different formal frameworks for the description of generalized probabilities in statistical theories. We analyze the particular cases of probabilities appearing in classical and quantum mechanics and the approach to generalized probabilities based on convex sets. We argue for considering quantum probabilities as the natural probabilistic assignments for rational agents dealing with contextual probabilistic models. In this way, the formal structure of quantum probabilities as a non-Boolean probabilistic calculus is endowed with a natural interpretation.

P. A. Meyer

Malcolm R. Forster

ABSTRACT: David Deutsch has a forthcoming article called “Quantum Theory of Probability and Decisions " in which he claims to derive the standard probabilistic interpretation of the wavefunction from non-probabilistic considerations. In this note, I try to develop his argument in a classical context, to see whether the same ideas can generate probabilistic conclusions from nonprobabilistic assumptions in a more general way. While my answer is negative, the attempt pinpoints the parts of Deutsch’s quantum mechanical argument that must rely on special features of the formalism (assuming that his proof is correct). 1. No Probabilities In, No Probabilities Out? You cannot derive an ‘ought ’ from an ‘is’. And I believe that it was Popper (1959) who once said, in response to those who think that randomness can be defined nonprobabilistically, that one cannot derive a probabilistic conclusion from non-probabilistic premises. Yet this is exactly what Deutsch (to appear) claims for quantum mechanical probabilities. Historically in the development of quantum theory, the Schrödinger

Gian‐Carlo Rota

Jincheng Zhang

This paper investigates the potential for a unified probabilistic framework based on quantum state dynamics, bridging the seemingly disparate realms of probability theory and quantum mechanics. We propose a novel approach that leverages the inherent dynamism of quantum states to redefine probability, offering a conceptual foundation for a more complete and consistent understanding of probabilistic processes. The core of this research lies in developing a probabilistic framework intrinsically linked to quantum mechanics, moving beyond traditional probability distributions to explore the fundamental relationship between quantum states and the underlying probability. The proposed mechanism centers on the observation that quantum states evolve through a continuous process of change, offering a pathway to a unified probabilistic representation. This work explores the implications of this framework for various applications, including quantum information theory and statistical mechanics. Ultimately, this paper lays the groundwork for a new approach to probabilistic theory, emphasizing the crucial role of quantum states in shaping the nature of probability.