Quantum suprematism picture of Malevich's squares triada for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics

TL;DR

This paper reviews the tomographic probability representation of quantum states, introduces new entropic inequalities, and develops a geometric approach using Malevich squares for visualizing qudit states, with applications to various quantum systems.

Contribution

It introduces a novel geometric visualization method for qudit states using Malevich squares and extends tomographic probability representation to include new entropic inequalities.

Findings

Derived new entropic-information inequalities for Franck--Condon factors.

Expressed density matrices of qudit states in terms of artificial qubit probabilities.

Developed a geometric approach to quantum states using Malevich squares.

Abstract

Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for Franck--Condon factors. Density matrices of qudit states are expressed in terms of probabilities of artificial qubits as well as the quantum suprematism approach to geometry of these states using the triadas of Malevich squares is developed. Examples of qubits, qutrits and ququarts are considered.