# Probability representation of quantum states as a renaissance of hidden variables -- God plays coins

## TL;DR

This paper presents a classical-like probabilistic framework for quantum states and observables, illustrating quantum superposition and interference through probability distributions, and reformulating quantum evolution as a kinetic equation.

## Contribution

It introduces a probability-based representation of quantum states, connecting quantum mechanics with classical statistical mechanics, and derives new formulas for quantum state interference.

## Key findings

- Probabilistic representation of quantum states and observables.
- Superposition principle expressed in terms of probabilities.
- Kinetic equation for quantum state evolution.

## Abstract

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An example of the spin-1/2 state is considered. We show that the triada of Malevich's squares can be used to illustrate the qubit state. We formulate the superposition principle of quantum states in terms of probabilities determining the quantum states. New formulas for nonlinear addition rules of probabilities providing the probabilities associated with the interference of quantum states are obtained. The evolution equation for quantum states is given in the form of a kinetic equation for the probability distribution identified with the state.