Teleporting an unknown qutrit state via a 2-qudit entangled channel

Abstract

We propose a quantum teleportation scheme for transmitting a single qutrit state by adopting a 2-qudit entangled state as the quantum channel. The measurement basis for Alice has been carefully and systematically constructed, which is essential for the successful implementation of the teleportation protocol. Based on Alice's measurement outcomes, we design the corresponding collective unitary transformations to be performed by Bob on an auxiliary qubit and information particle. After implementing the collective unitary transformation, Bob performs a von Neumann measurement on the auxiliary qubit. The single qutrit state is then teleported to the distant receiver Bob with a finite success probability. We obtain the achievable success probabilities of the proposed teleportation scheme for different quantum channels. The obtained results not only enrich the theory of quantum teleportation over high-dimensional entangled channels but also provide a novel and feasible approach to implementing qutrit teleportation.

Figures (1)

• Figure 1: The detailed quantum circuit of the quantum teleportation scheme is as follows. Initially, a qutrit (particle 1) is in an unknown quantum state $|\psi\rangle_1$ to be teleported. Both 4-level particles 2 and 3 are in the state $|0\rangle$. By performing a unitary operator $U_{1}$ on Alice's particle 2 and a joint unitary operator $U_2$ on particles 2 and 3, and sending the particle 3 to the receiver Bob, the quantum channel has been prepared. Then Alice makes a quantum measurement $\{M_i\}$ on the particles 1 and 2, and informs the receiver Bob her measurement outcome via a classical information channel. According to Alice's measurement result, Bob operates the corresponding collective unitary operator $U_{3b}^{(i)}$ on particle 3 and an auxiliary qubit $b$ with initial state $|0\rangle_{b}$. After that Bob makes a measurement on the auxiliary qubit $b$. If the measurement outcome is $|0\rangle_b$, then the quantum state of particle 3 is the unknown quantum state $|\psi\rangle$. The teleportation has been successfully realized.