Star Product Formalism for Probability and Mean Value Representations of Qudits

TL;DR

This paper develops a star-product formalism for representing qubits and qutrits in probability and mean value frameworks, enabling explicit calculations of quantum state and observable products.

Contribution

It extends the quantizer-dequantizer formalism to qudits, providing explicit star-product kernels for qubits and a framework for higher-dimensional systems.

Findings

Derived explicit star-product kernels for qubits.

Extended formalism to higher-dimensional qudits.

Facilitated calculations of quantum state and observable products.

Abstract

The quantizer-dequantizer formalism is developed for mean value and probability representation of qubits and qutrits. We derive the star-product kernels providing the possibility to derive explicit expressions of the associative product of the symbols of the density operators and quantum observables for qubits. We discuss an extension of the quantizer-dequantizer formalism associated with the probability and observable mean-value descriptions of quantum states for qudits.