Malevich’s Suprematist Composition Picture for Spin States

Abstract

This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch–Gordan Coefficients

“…The joint-probability-distribution entropic-information inequalities show correlations (or "hidden" correlations [6]) in bipartite systems, which is the reason to call the set of functions y(x 1 , x 2 ), x 1 (y), and x 2 (y) (1)-(3) the functions detecting hidden correlations.…”

“…, X k ). The function is used to describe hidden correlations [5][6][7] in quantum and classical systems that do not contain subsystems. The set of values of these functions and their arguments have the geometrical interpretation as the set of dots with integer nonnegative coordinates {x 1 , .…”