Quantum Teleportation of $n$ Qudits - Ideas?

[Quantum Question]

Homework Statement

Do a quantum teleportation protocol which teleports a state of n qudits given by:

\begin{equation}|\psi >_A := \sum_{p \in Z^n_D} \alpha_p |p>, \quad \quad \sum_{p \in Z^n_D} |\alpha_p|^2 = 1, \end{equation}

from Alice to Bob. It is supposed that in order to do it, Alice and Bob share n Bell pairs of qudits of the generic type :

with \begin{equation} i, j \in Z^n_D \end{equation}

and

​

chosen to satisfy:

and

Does anyone have any suggestions about how to start this problem? Thank you a lot in advance.

 

[BigJDubs]

Homework EquationsThe equations that you need to use for this problem are the quantum teleportation protocol which is given by: 1. Alice performs an entangling operation on her qudit state $| \psi \rangle_A$ and one of the Bell pairs she shares with Bob.2. Alice measures both qudits of the entangled pair and communicates the measurement results to Bob. 3. Bob performs a unitary operation on his qudit of the Bell pair depending on the measurement results communicated to him by Alice. The other equations you would need to use are the definition of the Bell pair states given by: \begin{equation} | \Phi^+ \rangle_{ij} = \frac{1}{\sqrt{D}} \sum_{k \in Z^n_D} |k \rangle_i |k \rangle_j \end{equation} and the definition of the entangling operation given by: \begin{equation} U = \sum_{m,n \in Z^n_D} |m \rangle \langle n|_A \otimes |m \rangle \langle n|_B \end{equation} where $U$ is the unitary operator that performs the entangling operation. The final equation you would need is the definition of the unitary operation that Bob performs depending on the measurement results communicated to him by Alice given by: \begin{equation} V_{pq} = \sum_{r \in Z^n_D} \omega^{-r\cdot(p-q)} |r \rangle \langle r| \end{equation}where $\omega$ is a primitive $D$-th root of unity and $V_{pq}$ is the unitary operator that Bob performs depending on the measurement results communicated to him by Alice.