Quantum Teleportation of a Single Qutrit using Two-Qutrit Entangled States

TL;DR

This work addresses the problem of teleporting a single qutrit by leveraging a complete set of two-qutrit entangled states derived from $SU(3)$ representation theory. It extends Bennett's protocol to a nine-channel framework, deriving a full set of non-unitary measurement operators $\\Lambda_i^k$ that enable end-to-end teleportation across all channels. The principal contributions are the explicit construction of the nine SU(3)-based entangled resources, the decomposition of the joint state into channel- and multiplicity-specific components, and the demonstration that non-unitary measurement gates are necessary in high-dimensional teleportation. The findings have implications for high-dimensional quantum communication and motivate measurement-based quantum computing approaches using qutrit systems, while also highlighting environmental and noise-related considerations that merit future investigation.

Abstract

We demonstrate quantum teleportation of a qutrit system using a complete set of two-qutrit entangled states obtained from the representation theory of the SU(3) group. All measurement gates essential for end-to-end teleportation are systematically evaluated, and these are found to be non-unitary. Our approach extends Bennett's teleportation protocol to the qutrit system with minimal modifications, preserving operational simplicity and underscoring the necessity of non-unitary measurement operators in high-dimensional systems.

Figures (1)

• Figure 1: Schematic diagram of qutrit teleportation from $\ket{\phi}_{A_1}$ to $\ket{\phi}_{B}$ using nine two-qutrit entangled states $\ket{\Psi_{i}}_{A_2B}$ shared between Alice and Bob following an augmented version of Bennett's protocol. Here, Alice's sector contains nine states $\ket{\Psi_{k}}_{A_1A_2}$ for each channel, while Bob's sector features pre-measurement states $\ket{s_{i}^k}_B$ and non-unitary measurement operators $\Lambda^{k}_{i}$, all consistent with SU(3) symmetry.