Construction of three-dimensional version of the amplitude damping channel

Qutrit is a three-level quantum system with a higher level than qubits, which can process quantum information in a more complex state space. Therefore, in some information processing tasks, qutrits are more efficient than qubits. In this paper, we first briefly review the basic knowledge of qubit and extend it to the qutrit scenario. Then, the noiseless qutrit channel is given by simple extension, and the transmission characteristics between it and the noiseless qubit channel are discussed. Subsequently, we provided a three-dimensional version of the amplitude damping channel based on its construction method. In this paper we will refer to it as the noisy qutrit channel \({\mathcal {N}}(\rho )\) $\mathcal{N}(\rho )$ . Finally, we discuss the transmission characteristics of \({\mathcal {N}}(\rho )\) $\mathcal{N}(\rho )$ and the amplitude damping channel, as well as the expected fidelity and entanglement fidelity of \({\mathcal {N}}(\rho )\) $\mathcal{N}(\rho )$ . What’s interesting is that we find whether it is a noisy channel or a noiseless channel, the qutrit channel can send qubit information, but the qubit channel cannot send qutrit information completely. The special case in which the qubit channel can send qutrit information completely is when the input qutrit state is \({|{0}\rangle }\) $|0⟩$ or \({|{1}\rangle }\) $|1⟩$ or a linear combination of \({|{0}\rangle }\) $|0⟩$ and \({|{1}\rangle }\) $|1⟩$ .