Table 1.

An example of Bob’s operation on his encoded information when $d=3$ and the result of the measurement is $|{\Phi }_{3i+j}\rangle$. According to their bases choice and the measurement result, it is necessary to retrieve his information for sharing the same information.

Bases	Bob’s Operation ($|{\mathbf{\Phi }}_{3\mathit{i}+\mathit{j}}\rangle$)
bases 1 ($l_x$, $p_y$)	$y\to y-i$ (mod 3)
	$1\leftrightarrow 2$ for $j=0$
bases 2 (${\overline{l}}_x$, ${\overline{p}}_y$)	$0\leftrightarrow 2$ for $j=1$
	$0\leftrightarrow 1$ for $j=2$