\{{\left | a_0 b_0 \right\rangle}\}, \{{\left | a_0 b_0 \right\rangle}\}, \{{\left | a_0 b_0 \right\rangle}\}, \{\mathcal{P}_0 {\left | a_0 b_0 \right\rangle}\}, \{\mathcal{P}_0 {\left | a_0 b_0 \right\rangle}\}