Multi-Bloch Vector Representation of the Qutrit

TL;DR

This paper introduces a novel multi-vector approach for representing qutrit quantum states, using three qubit-like Bloch vectors, which enhances the description of higher-dimensional quantum systems.

Contribution

It proposes a new method of representing qutrit states with multiple Bloch vectors, extending the Bloch sphere concept beyond qubits.

Findings

Qutrit states can be described by three qubit-like Bloch vectors.

The approach provides a more comprehensive representation of higher-dimensional quantum states.

It offers a potential framework for better visualization and analysis of qutrits.

Abstract

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.