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Studies on Bell's theorem.

机译:贝尔定理的研究。

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In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one.;The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24].;In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26].;In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems.;Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6].;According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible quantities are not allowed by classical mechanics, a feature that is called as "quantum nonlocality". An experimental observation of those correlations, in other words, a violation of the limits imposed by classical physics, implies the correctness of quantum description and invalidates the classical, local realistic models.;The first Bell experiments were proposed by Clauser, Horne, Shimony, and Holt, who invented the most famous Bell's inequality [13]. Later, the Aspect experiments were satisfactory enough for the physics community to be conclusive about the validation of quantum mechanics [1][3][4][2].;Ekert's work on applications of quantum nonlocality to communication resulted in the new field of quantum communication and cryptography, and turned the research program into a practical one [20].;Pitowsky showed a method to fi all expressions of limitations due to local realism, all Bell's inequalities, for a given physical scenario. He also proved that the problem is, unfortunately, NP-complete and hence as the scenarios get more complex, they also become computationally intractable [33][34]. Therefore, different methods for the solution of special cases of the problem are necessary.;Inequalities found for those special cases can be called classes of Bell's inequalities. For example, Werner and Wolf [41] and Collins, Gisin, Linden, Massar, and Popescu [16] found classes that cover a wide range of scenarios.;Our work is a similar kind of effort to produce and study new types of Bell's inequalities.
机译:在这项工作中,我们寻找贝尔不等式的新颖类别和产生它们的方法。我们还发现了它们的量子违规,如果可能的话,包括最大的违规。我们在第二章中解释的约旦基数方法是关于使用一对特定类型的正交基数,它们的跨度是与不相容量的测量结果相关的子空间。相同的物理系统。 Jordan向量是表达任何两个子空间的相对方向的最简单方法。此功能可帮助我们减少进行优化的参数空间的维数。该著作发表在[24]中。在第三章中,我们试图找到群论与贝尔定理之间的联系。我们设计了一种生成与代数群的元素有关的贝尔不等式的项的方法。同一组生成Bell不等式的项和可用于计算Bell表达式的量子值的可观测项。简而言之,贝尔定理是由爱因斯坦,波多尔斯基,罗森[19]和玻尔[8]在量子力学的早期阶段启动的一项研究程序的主要工具,我们的结果发表在[25] [26]中。在讨论物理系统的核心本质时。这些争论是关于一种新型的称为叠加态的物理状态,它是由量子力学引入的,并表现为在同样准备好的系统的测量结果中不可避免地存在随机性;贝尔的巨大贡献是寻找一种量化问题的方法,因此通过将问题改写为对空间上分开的系统的测量结果之间的某些相关性组合的限制来打开实验验证之路[7]。多亏了贝尔,与量子力学系统性质有关的基本问题才得以量化[6]。根据贝尔定理,经典力学不允许量子纠缠系统之间涉及不相容量的某些相关性。 “量子非局部性”。对这些相关性的实验观察,换句话说,违反了经典物理学的限制,这暗示了量子描述的正确性,并使经典的局部现实模型无效。;第一个Bell实验是由Clauser,Horne,Shimony,霍尔特(Holt)发明了最著名的贝尔不等式[13]。后来,Aspect实验对于物理学界来说足以令人满意地就量子力学的验证做出结论[1] [3] [4] [2] 。; Ekert在量子非局域性在通信中的应用工作开创了新的领域。量子通信和密码学,并将研究程序变成了一个实用的程序[20] 。;皮托斯基展示了一种方法,可以在给定的物理情况下,解决由于局部真实性和所有贝尔不等式而引起的所有局限性表达。他还证明了不幸的是,问题是NP完全的,因此随着场景变得越来越复杂,它们在计算上也变得难以处理[33] [34]。因此,有必要采用不同的方法来解决问题的特殊情况。这些特殊情况下发现的不等式可以称为Bell不等式类。例如,沃纳和沃尔夫[41]以及柯林斯,吉辛,林登,马萨尔和波佩斯库[16]发现了涵盖广泛场景的课程。我们的工作是类似的努力,以产生和研究新型的贝尔不平等。

著录项

  • 作者

    Guney, Veli Ugur.;

  • 作者单位

    City University of New York.;

  • 授予单位 City University of New York.;
  • 学科 Theoretical physics.;Physics.
  • 学位 Ph.D.
  • 年度 2015
  • 页码 200 p.
  • 总页数 200
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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