A CH-type Inequality For Real Experiments

We derive an efficient CH-type inequality. Quantum mechanics violates our proposed inequality independent of the detection-efficiency problem. In photonic Bell-type experiments [1], when photon pairs with parallel linear polarizations are emitted, one can consider a Clauser-Horne (CH) inequality [2], at the level of hidden variables, in the form − 1 ≤ Srq,HV (â, b̂, â, b̂, λ) ≤ 0 (1) where Srq,HV (â, b̂, â, b̂, λ) = p (1) r (â, λ) [ p q (b̂, λ)− p (2) q (b̂ , λ) ] +p r (â , λ) [ p q (b̂, λ) + p (2) q (b̂ , λ) ] −p r (â , λ)− p q (b̂, λ) (2) In (2), we are considering four sub-ensemble of photon pairs with linear polarizations along (â, b̂), (â, b̂), (â, b̂), and (â, b̂) in which one registers ∗E-mail: [email protected]