God plays coins or superposition principle for classical probabilities in quantum suprematism representation of qubit states

TL;DR

This paper explores a novel quantum representation of classical coin probabilities using spin-$1/2$ states and Malevich's squares, revealing a superposition principle as a nonlinear addition rule for classical probabilities.

Contribution

It introduces a quantum-like framework for classical probabilities, linking them to quantum density matrices and superposition principles in a geometric representation.

Findings

Quantum density matrices constructed from classical coin probabilities.

Superposition principle expressed as a nonlinear addition rule.

Geometric visualization using Malevich's squares.

Abstract

For three given probability distributions describing positions of three classical coins the quantum density matrix of spin-$1/2$ state is constructed and its matrix elements are associated with triada of Malevich's squares. The superposition principle of spin-$1/2$ states is presented in the form of nonlinear addition rule for these classical coin probabilities. We illustrate the formulas by the statement"God does not play dice - God plays coins".