On the properties of qudits

TL;DR

This paper reviews the properties of qudits, especially in the context of quantum information applications in astrophysics, highlighting differences from qubits and exploring new properties in higher dimensions.

Contribution

It provides a comparative analysis of one- and two-qudit systems, emphasizing how properties extend or differ from qubits, including the characterization of Werner states in higher dimensions.

Findings

Two-qubit Werner states can be pure, unlike higher-dimensional Werner states.

Properties of two-qubit systems do not always generalize to qudits.

New properties emerge for dimensions three or higher.

Abstract

Motivated by the growing interest in the applications of quantum information science in astrophysical settings, especially for the neutrino transport in compact objects where three-flavors of neutrinos need to be mapped on qutrits, we review properties of one- and two-qudit systems. We contrast two-qubit and two-qudits systems by pointing out how some of the properties of two-qubit systems generalize to higher dimensions and explore emerging new properties for dimensions three or higher. One example is provided by the Werner states: when the density operator is written in the fundamental representation, we show that only two-qubit Werner states can be pure states, but not two-qudit Werner states when the qudit dimension is larger than two.