On the violation of Bell's inequality for all non-product quantum states
Carlo Cafaro, Sean Alan Ali, Adom Giffin
备注：
12 pages, no figures. We have added the following sentence in the arXiv-version (Section named: Background): The following background discussion follows very closely the presentation presented by Asher Peres in Ref. [13]. Ref. [13] (together with References [1], [14], and [16]) by Asher Peres was already present in the published version of our manuscript
We present an explicit reexamination of Gisin's 1991 original proof concerning the violation of Bell's inequality for any pure entangled state of two-particle systems. Given the relevance of Gisin's work, our analysis is motivated by pedagogical reasons and allows the straightening of a few mathematical points in the original proof that in no way change the physical conclusions reached by Gisin.
Bell's inequality has been derived several times from quite different basic assumptions, which imply different conclusions. This resulted into widespread confusion regarding the exact implications of the experimental violations of the inequality. In this article, the structures of Bell's and of Peres' derivations are analyzed, and the title question is explicitly answered.
We report Bell violations with classical light prepared in both entangled and non-entangled polarization-path, binary states. Our results show that violations of constraints such as the Bell-Clauser-Horn-Shimony-Holt inequality do not necessarily falsify local-realism. Correlations in the realm of classical statistical optics, which are not of the Bell type, may lead to Bell violations.
We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.
In this article, we analyse the relationship between the Bell violation and the secure key rate of entanglement assisted quantum key distribution (QKD) protocols. Specifically, we address the question whether Bell violation is necessary or sufficient for secure communication. We construct a class of states which do not show Bell violation, however, which can be used for secure communication after local filtering. Similarly, we identify another class of states which show Bell violation but can not be used for generating secure key even after local filtering. The existence of these two classes o…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality. We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities. We further show that Bell-type inequalities for relative …
We study an asymmetric form of two-mode entangled coherent state (ECS), where the two local amplitudes have different values, for testing the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We find that the asymmetric ECSs have obvious advantages over the symmetric form of ECSs in testing the Bell-CHSH inequality. We further study an asymmetric strategy in distributing an ECS over a lossy environment and find that such a scheme can significantly increase violation of the inequality.
Experimental Bell inequality violation without the postselection loophole
本文报道了利用能量-时间纠缠光子对Bell-Clauser-Horne-Shimony-Holt（Bell-CHSH）不等式的实验违反。该实验并非没有局部性和检测漏洞，而是第一次使用能量-时间纠缠光子违反Bell-CHSH不等式，该光子不存在由April等人描述的后选择漏洞[Phys. Rev. Lett. 83，2872（1999）]。
We investigate a classical statistical model and show that Mermin's version of a Bell inequality is violated. We get this violation, if the measurement modifies the ensemble, a feature, which is also characteristic for measurement processes for quantum systems.
By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these ontological states as the ones embedded with realism and compare them to the (usual) quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell's inequality: the usual inequality cannot be applied to the usual experiments. We buil…
By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.
