Short-Distance Bidirectional Teleportation for Arbitrary Unknown Single-Qutrit States in Noise Environment

The purpose of this article is to further investigate short-distance quantum teleportation (QT). First, we construct a two-particle three-dimensional (3D) Bell state by utilizing the Hadamard transforms and controlled NOT transforms in a 3D quantum system. Then, we put forward a deterministic 3D protocol of bidirectional QT (BQT) of arbitrary unknown single-qutrit states for short-distance communicators in an ideal environment. In this BQT protocol, the 3D quantum channel is composed of a 3D-Bell state and an auxiliary qutrit in initial state |0⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|0\rangle $$\end{document}, and two communicators can exchange their arbitrary single-qutrit states simultaneously by using 3D unitary transformations. Subsequently, we investigate the performance of the deterministic short-distance BQT scheme under the 3D Pauli-class noise channel where the noise error includes t-depolarizing, t-phase-flip, trit-flip and trit-phase-flip, and provide analytical formulas for quantifying average fidelity based on four types of noise channels. The results indicate that regardless of the type of noise, the state independent average fidelity (SIAF) is always a linear function of the noise parameter, and this function decreases as the noise parameter increases. Among these noise errors, triple-flip and triple-phase-flip have the highest SIAF, while t-phase-flip has the lowest SIAF. Although our protocol is suitable for transmission in a small range, it has potential application prospects, especially in saving quantum resources.