From quantum carpets to quantum suprematism-the probability representation of qudit states and hidden correlations

We develop the tomographic-probability picture where quantum states of qudits (spin-j systems, N-level atoms) are described by means of sets of fair classical probability distributions associated with properties of sets of dichotomic classical random variables. We formulate the superposition principle of pure quantum states as nonlinear addition rule of standard probabilities. The invertible map of the density matrices of qudit states onto the probability distributions is illustrated by their geometric representation in terms of triangles and squares called Malevich's squares. We discuss an analogy of the squares with the quantum carpet picture. New entropic inequalities obtained due to the introduced map of the density matrices onto Malevich's squares are studied. The correlations in systems without subsystems (hidden correlations) are discussed.