aqora

Expectation Value in Bell's Theorem

Zheng-Chuan Wang

We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented, which is coincided with the prediction of quantum mechanics.We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell's inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experiments to show the violation of Bell's inequality and then further deny the local hidden-variables theory. Considering the difference of their expectation values, a generalized Bell's inequality is presented, which is coincided with the prediction of quantum mechanics.

arXiv:quant-ph/0604194Apr 26, 20060 citations

The Bell inequalities and nonlocality

Peter Rastall

Physics Letters AJan 1, 19823 citations

New Method to Reveal the Conflict Between Local Realism and Quantum Mechanics

Koji Nagata, Jaewook Ahn

We formulate the expectation value of the Bell-Zukowski operator acting on qubit states of a two-particle Bell experiment. By using the equivalence between a set of N copies of a two-qubit experiment and a standard two-setting Bell experiment in an entangled 2N-particle state, we obtain an inequality, which we may call the Bell-Zukowski inequality. It determines whether the measured correlation functions of two-particle states can be modeled locally and realistically. In this Bell experiment of two particles, the conflict between local realism and quantum mechanics is discussed in conjunction with the violation of the Bell-Zukowski inequality. The main point of the result is that the Bell-Zukowski operator can be represented by the Bell-Mermin operator. The threshold visibility of two-particle interference analyzed in this scheme shows good agreement with the value to cause a violation of the Bell-Zukowski inequality.We formulate the expectation value of the Bell-Zukowski operator acting on qubit states of a two-particle Bell experiment. By using the equivalence between a set of N copies of a two-qubit experiment and a standard two-setting Bell experiment in an entangled 2N-particle state, we obtain an inequality, which we may call the Bell-Zukowski inequality. It determines whether the measured correlation functions of two-particle states can be modeled locally and realistically. In this Bell experiment of two particles, the conflict between local realism and quantum mechanics is discussed in conjunction with the violation of the Bell-Zukowski inequality. The main point of the result is that the Bell-Zukowski operator can be represented by the Bell-Mermin operator. The threshold visibility of two-particle interference analyzed in this scheme shows good agreement with the value to cause a violation of the Bell-Zukowski inequality.

arXiv:0811.3275Journal of the Korean Physical SocietyDec 15, 20080 citations

A Derivation of a Weaker, Local Bell inequality

M. R. Clover

Bulletin of the American Physical SocietyMar 6, 20070 citations

Generalized Bell’s inequalities

Luigi Schiavulli

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoNov 1, 19772 citations

Bell nonlocality with a single shot

Mateus Araújo, Flavien Hirsch, Marco Túlio Quintino

In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p -value it will give for a physical experiment. Here we show that to obtain a small expected p -value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and Inn22 inequalities.We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small p -value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p -value it will give for a physical experiment. Here we show that to obtain a small expected p -value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and Inn22 inequalities.We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small p -value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.

arXiv:2005.13418QuantumOct 28, 202025 citations

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