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Register a new userBell inequalities versus quantum physics: A reply to Lambare
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Robert B. Griffiths
Publication date
2021
fields
Physics
and research's language is
English
Authors
Robert B. Griffiths
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In Phys. Rev. A 101 (2020) 022117 it was argued that Bell inequalities are based on classical, not quantum, physics, and hence their violation in experiments provides no support for the claimed existence of peculiar nonlocal and superluminal influences in the real (quantum) world. Following a brief review of some aspects of the Consistent Histories approach used in that work, the objections raised in Lambares Comment, arXiv:2102.075243v3, are examined and shown to rest on serious misunderstandings, and as a result fail to identify any errors in, or problems with, the work being criticized.
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Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum cryptography and tomography or self-testing. Building upon a series of recent works on the geometry of quantum correlations, we are interested in the problem of computing quantum Bell inequalities or the boundary between quantum and post-quantum world. Better knowledge of this boundary will lead to more efficient device-independent quantum processing protocols. We show that computing quantum Bell inequalities is an instance of a quantifier elimination problem, and apply these techniques to the bipartite scenario in which each party can have three measurement settings. Due to heavy computational complexity, we are able to obtain the characterization of certain linear relaxation of the quantum set for this scenario. The resulting quantum Bell inequalities are shown to be equivalent to the Tsirelson-Landau-Masanes arcsin inequality, which is the only type of quantum Bell inequality found since 1987.
We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell inequalities and quantum Bell inequalities in bipartite scenarios with dichotomic observables. We discuss how to improve the latter approximation and how to extend our ideas to scenarios with more than two outcomes per setting.
We describe a method of extending Bell inequalities from $n$ to $n+1$ parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is non trivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerfull indicators of non-classical correlations than the original inequalities.
We review in this paper the research status on testing the completeness of Quantum mechanics in High Energy Physics, especially on the Bell Inequalities. We briefly introduce the basic idea of Einstein, Podolsky, and Rosen paradox and the results obtained in photon experiments. In the tests of Bell inequalities in high energy physics, the early attempts of using spin correlations in particle decays and later on the mixing of neutral mesons used to form the quasi-spin entangled states are covered. The related experimental results in K^0 and B^0 systems are presented and discussed. We introduce the new scheme, which is based on the non-maximally entangled state and proposed to implement in phi factory, in testing the Local Hidden Variable Theory. And, we also discuss the possibility in generalizing it to the tau charm factory.
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a unique coordination game. In the simplest case, Alice and Bob, each having two random variables, attempt to maximize the area of a rectangle and the rectangles area is represented by a certain parameter. This parameter, which is a function of the correlations between their random variables, is shown to be a Bell parameter, i.e. the achievable bound using only classical correlations is strictly smaller than the achievable bound using non-local quantum correlations We continue by generalizing to the case in which Alice and Bob, each having now n random variables, wish to maximize a certain volume in n-dimensional space. We term this parameter a multiplicative Bell parameter and prove its Tsirelson bound. Finally, we investigate the case of local hidden variables and show that for any deterministic strategy of one of the players the Bell parameter is a harmonic function whose maximum approaches the Tsirelson bound as the number of measurement devices increases. Some theoretical and experimental implications of these results are discussed.
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