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arXiv:quant-ph/0401022 · Journal of Modern Optics

A CH-type inequality for real experiments

A. Shafiee

Published Apr 1, 2004• 3 citations
arXivHTMLPDF

Abstract

We derive an efficient CH-type inequality. Quantum mechanics violates our proposed inequality independent of the detection-efficiency problem.
DOI
10.1080/09500340408233629

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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 where − 1 ≤ Srq,HV (â, ̂ b, â ′ , ̂ b ′ , λ) ≤ 0 (1) Srq,HV (â, ̂b, â ′ , ̂ b ′, λ) = p (1) r (â, λ) p (2) q (̂b, λ) − p (2) q ( ̂ b ′, λ)] +p (1) r ( â ′ , λ) [ p (2) q ( ̂b, λ) + p (2) q ( ̂ b ′, λ)] −p (1) r (â ′ , λ) − p (2) q ( ̂ b, λ) (2) In (2), we are considering four sub-ensemble of photon pairs with linear polarizations along (â, ̂ b), (â, ̂ b ′), ( â ′ , ̂ b), and ( â ′ , ̂ b ′ ) in which one registers
In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role. Here, we want to show that the interpretation of these experiments could be feasible, if some different alternative assumptions other than the fair sampling were used. For this purpose, we derive an efficient Bell-type inequality which is a CHSH-type inequality in real experiments. Quantum mechanics violates our proposed inequality, independent of the detection-efficiency problems.
Quantum nonlocality can be tested in experiments via the violation of the Bell inequality. We propose novel methods of the rearrangement and linear inequality to prove all the known Bell-CH inequalities of Imn22Imn22Imn22-type (m,n≤5m,n\le5m,n≤5). We also derive a set of new Bell-CH inequalities by using these methods which should be violated in quantum entangled states.