Spin tomography and star-product kernel for qubits and qutrits

TL;DR

This paper develops a unified framework for spin tomography of qubits and qutrits using tensor operators, providing explicit forms of quantizers, dequantizers, and star-product kernels, enhancing the mathematical tools for quantum state reconstruction.

Contribution

It introduces explicit quantizer and dequantizer operators and derives the star-product kernel for qubits and qutrits, linking different spin tomogram forms.

Findings

Explicit quantizer and dequantizer operators for low-spin states

Star-product kernel derived for qubits and qutrits

Connection established with a general star-product formula

Abstract

Using the irreducible tensor-operator technique, we establish the relation between different forms of spin tomograms. Quantizer and dequantizer operators are presented in simple explicit forms and are specified for the low-spin states. The kernel of the star-product is evaluated for qubits and qutrits and its connection with a generic formula is found.