Exact target-adapted endpoint transport

Choose sender and receiver positions $x_A,x_B\in U$ with developed separation

Assume the full straight developed segment lies in the regular laboratory. Install $n+1$ sites at

Each site has a two-qubit payload register $X_j\cong {\mathbb{C}}^4$. Prepare $X_1,\dots ,X_n$ in a fixed pure blank $\omega$. At hop $j$, SWAP $X_{j-1}$ with $X_j$. The externally prescribed tick duration is