Correlations in a system of classical-like coins simulating spin-1/2 states in the probability representation of quantum mechanics

An analog of classical “hidden variables” for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical-like coins. The bijective map of the states corresponds to the presence of correlations of random classical-like variables associated with the coin positions “up” or “down” and the observables are mapped onto quantum observables described by Hermitian matrices. The connection of the classical-coin statistics with the statistical properties of qubits is found. Graphical abstract