[$$\begin{array}[c]{lllllllllllllll}
\ket e = X^{x_1} Z(\theta_1) \otimes \ldots \otimes  X^{x_l} Z(\theta_l) \ket I
\end{array}$$]{} and the remaining qubits in the following form [$$\begin{array}[c]{lllllllllllllll}
\forall i\in D &\;\;\;& \ket {d_i} \\ 
\forall i \not \in D &\;\;\;& \prod_{j\in N_G(i) \cap D} Z^{d_j}\ket {+_{\theta_i}}
\end{array}$$]{} and sends the Server all the $3N (3c+1)$ qubits in the order of the labelling of the graph.

– **Server’s move:** Server receives $3N(3c+1)$ single qubits and entangles them according to $DT(G)$.

$\bullet$ **Step $i : \; 1 \leq i \leq 3N (3c+1)$**

– **Client’s move:** Client computes the angle $\delta_i = C(i, \phi_i, \theta_i, r_i, \mathbf{s})$ and sends it to the Server.\
– **Server’s move:** Server measures qubit $i$ with angle $\delta_i$ and sends the result $b_i$ to the Client.\
– **Client’s move:** Client sets the value of $s_i$ in $\mathbf{s}$ to be $b_i + r_i$.\
$\bullet$ **Final Step:**

– **Server’s move:** Server returns the last layer of qubits (output layer) to the Client.\
$\bullet$ \[step:Alice-prep\] **Verification**\
– After obtaining the output qubits from the Server, the Client measures the output trap qubits with angle $\delta_t = \theta_t + r_t \pi$ to obtain $b_t$.

– Client accepts if $b_i = r_i$ for all the white (primary) 