Invariant Vector and Majorana Star Representations of Qutrit States

TL;DR

This paper introduces a 3D invariant vector representation for qutrit states, demonstrating its advantages and relating it to the Majorana star representation, thereby simplifying visualization of complex quantum states.

Contribution

It presents the time-evolution of invariant vector representation for qutrits and connects it with the Majorana star representation, enhancing understanding of qutrit state dynamics.

Findings

IVR vectors effectively visualize qutrit states

Relation established between IVR and Majorana star representations

Demonstrated advantages of IVR in state evolution analysis

Abstract

The Qutrit state density matrix is of order 3 and depends on 8 parameters in general case. Visualization of this 8-dimensional state space is practically impossible using 8-dimensional vectors commonly used. Recently a 3-dimensional vector representation of the Qutrit state space (also called Invariant Vector Representation) has been proposed [1]. In this work we present the time-evolution of the IVR vectors for the Qutrit Cascade or {\Xi}-model to emphasize the advantages of the IVR and also relate IVR vectors to well-known stars of the Majorana State Representation (MSR).