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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Nonlocal theories satisfying bell’s inequality

P. Selleri, Gino Tarozzi

Published Nov 1, 1978• 7 citations
Publisher
DOI
10.1007/bf02748654

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In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of local (subluminal) hidden variables, but it cannot be satisfied in the general case within standard quantum mechanical formalism or within theories of nonlocal (superluminal) hidden variables. It is shown too that within theories of nonlocal hidden variables but not in the standard quantum mechanical formalism a paradox appears in the situation when one of the correlated subsystems arrives at a Schwarzschild black hole. Namely, there is no way that black hole horizon obstructs superluminal influences between spin of the subsystem without horizon and spin of the subsystem within horizon,or simply speaking,there is none black hole horizon nor "no hair" theorem for subsystems with correlated spins. It implies that standard quantum mechanical formalism yields unique consistent and complete description of the quantum mechanical phenomenons.

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Several foundational and information theoretic implications of Bell’s theorem

Guruprasad Kar, Manik Banik

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality. He also showed that QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review, we will discuss various foundational as well as information theoretic implications of BI. We will also discuss about some restricted nonlocal feature of quantum nonlocality and elaborate the role of Uncertainty principle and Complementarity principle in explaining this feature.

arXiv:1408.0526•International Journal of Quantum Information•Aug 18, 2016•5 citations
In this work a general relativistic generalization of Bell inequality is suggested. Namely,it is proved that practically in any general relativistic metric there is a generalization of Bell inequality.It can be satisfied within theories of local (subluminal) hidden variables, but it cannot be satisfied in the general case within standard quantum mechanical formalism or within theories of nonlocal (superluminal) hidden variables. It is shown too that within theories of nonlocal hidden variables but not in the standard quantum mechanical formalism a paradox appears in the situation when one of the correlated subsystems arrives at a Schwarzschild black hole. Namely, there is no way that black hole horizon obstructs superluminal influences between spin of the subsystem without horizon and spin of the subsystem within horizon,or simply speaking,there is none black hole horizon nor "no hair" theorem for subsystems with correlated spins. It implies that standard quantum mechanical formalism yields unique consistent and complete description of the quantum mechanical phenomenons.
Measurement incompatibility and quantum nonlocality are two key features of quantum theory.Violations of Bell inequalities require quantum entanglement and incompatibility of the measurements used by the two parties involved in the protocol.We analyze the converse question: for which Bell inequalities is the incompatibility of measurements enough to ensure a quantum violation?We relate the two questions by comparing two tensor norms on the space of dichotomic quantum measurements, one characterizing measurement compatibility and the other characterizing violations of a given Bell inequality.We provide sufficient conditions for the equivalence of the two notions in terms of the matrix describing the correlation Bell inequality.We show that the Clauser-Horne-Shimony-Holt inequality and its variants are the only ones that satisfy it.
In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality. He also showed that QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review, we will discuss various foundational as well as information theoretic implications of BI. We will also discuss about some restricted nonlocal feature of quantum nonlocality and elaborate the role of Uncertainty principle and Complementarity principle in explaining this feature.