1. 例 1 f≡0:Step 2 态不变;(1/2)·Σ_x|x⟩ = H^⊗2|00⟩,而 H^⊗2·H^⊗2 = I → |ψ₃⟩ = |00⟩,P(00) = 1
2. 例 1 补注:f≡1 只差全局相位 −1,测量结果与 f≡0 完全相同
3. 例 2 Step 2:|ψ₂⟩ = ½(|00⟩+|01⟩−|10⟩−|11⟩),系数 (+1,+1,−1,−1) 对应 x=00,01,10,11
4. 例 2 Step 3 逐基矢归并(用 H^⊗2|x⟩ 的四个展开式):
A(|00⟩) = ¼(1+1−1−1) = 0;A(|01⟩) = ¼(1−1−1+1) = 0;A(|10⟩) = ¼(1+1+1+1) = 1;A(|11⟩) = ¼(1−1+1−1) = 0
5. 验证行:0²+0²+1²+0² = 1 ✓;测得 10 ≠ 00 → 判平衡