- 命题框:Z₀Z₁ = Z⊗Z,测量结果 = 两个比特各自 Z 读数之积(联合测量,不是单比特测量)
- 方法一(公式法,逐行):
1. (Z⊗Z)|Φ⁺⟩ = (1/√2)[(+1)(+1)|00⟩ + (−1)(−1)|11⟩] = (1/√2)(|00⟩ + |11⟩) = |Φ⁺⟩
2. |Φ⁺⟩ 是 Z⊗Z 的本征态、本征值 +1 → ⟨Z₀Z₁⟩ = ⟨Φ⁺|Φ⁺⟩ = 1
- 方法二(概率法,逐项):结果 00(P = 1/2,积 (+1)×(+1) = +1)+ 结果 11(P = 1/2,积 (−1)×(−1) = +1)+ 结果 01/10(P = 0)→ (+1)(1/2) + (+1)(1/2) = 1
- 结果框(大数字 1):⟨Z₀⟩ = 0、⟨Z₁⟩ = 0,但 ⟨Z₀Z₁⟩ = 1——单独无信息、联合完全正相关;贝尔态强关联的定量刻画