Kolmogorovian Censorship Hypothesis For General Quantum Probability Theories

Luigi Accardi

Diederik Aerts

Luigi Accardi

Andrei Yu. Khrennikov

Philippe Grangier

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness-the view that the quantum state is operationally incomplete until the measurement context is specified-provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov's to Gleason's framework for quantum probabilities.

László E. Szabó, Márton Gömöri, Zalán Gyenis

According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative frequencies expressible in operational terms using classical Kolmogorovian probability theory. In other words, a quantum theoretical description of a system should in principle be translatable into a purely operational-probabilistic description. However, our goal in this paper is different; we do not want to deal with the problem how to translate the known theory of quantum mechanics into operational terms, or to reconstruct the theory from postulates which can be interpreted in operational terms. Our aim is somewhat broader and points in the opposite direction. We start with a general scheme for the operational description of an arbitrary physical system. The description is based solely on the notion of observable events (measurement operations and measurement results) and on general, empirically established simple laws concerning their relative frequency. These laws are so simple and fundamental that they apply equally to any physical system. In the first part of the paper, we outline the basic elements of such an operational-probabilistic theory. In the second part, we discuss how this operational-probabilistic description compares to the quantum mechanical description and to what extent the standard Hilbert space quantum mechanics can be regarded as a reformulation of the general operational-probabilistic theory.