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Chinese Physics Letters

Bell Operator Method to Classify Local Realistic Theories

Koji Koji, Nagata

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

我们与背景的一个任意的数字考察多国参加的贝尔不平等的历史的事实。为一个关联函数的值的一个明确的本地现实主义的模型，交上一个二背景的贝尔实验(二背景的模型)，仅仅为在给定的实验的设置的特定的集合的工作，但是不能为一个关联函数的值构造一个本地现实主义的模型，交上一个连续无限的设置贝尔实验(无限背景的模型)，尽管在那里存在为在空格的所有方向的二背景的模型。因此，二背景的模型没有无限背景的模型有的性质。这里，我们证明一个明确的二背景的模型不能为关联功能的价值构造一个本地现实主义的模型，交上一个 M 背景贝尔实验(M 背景模型) ，尽管在那里存在为在给定的 M 背景选择的 M 测量方向的二背景的模型试验。因此，二背景的模型没有 M 背景模型有的性质。

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我们与背景的一个任意的数字考察多国参加的贝尔不平等的历史的事实。为一个关联函数的值的一个明确的本地现实主义的模型，交上一个二背景的贝尔实验(二背景的模型)，仅仅为在给定的实验的设置的特定的集合的工作，但是不能为一个关联函数的值构造一个本地现实主义的模型，交上一个连续无限的设置贝尔实验(无限背景的模型)，尽管在那里存在为在空格的所有方向的二背景的模型。因此，二背景的模型没有无限背景的模型有的性质。这里，我们证明一个明确的二背景的模型不能为关联功能的价值构造一个本地现实主义的模型，交上一个 M 背景贝尔实验(M 背景模型) ，尽管在那里存在为在给定的 M 背景选择的 M 测量方向的二背景的模型试验。因此，二背景的模型没有 M 背景模型有的性质。
We review the historical fact of multipartite Bell inequalities with an arbitrary number of settings. An explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment (two-setting model), works only for the specific set of settings in the given experiment, but cannot construct a local realistic model for the values of a correlation function, given in a continuous-infinite settings Bell experiment (infinite-setting model), even though there exist two-setting models for all directions in space. Hence, the two-setting model does not have the property that the infinite-setting model has. Here, we show that an explicit two-setting model cannot construct a local realistic model for the values of a correlation function, given in an M -setting Bell experiment ( M -setting model), even though there exist two-setting models for the M measurement directions chosen in the given M -setting experiment. Hence, the two-setting model does not have the property that the M -setting model has.
量子力学是在物理学里最成功和最精巧的理论之一,它只在一段相当短的时间里就建立起来了.历史上有许多重要的物理学理论是由很少数的几个人创立的,而这些理论都没有引起任何重大的争论.几个著名的例子是由牛顿创立的力学,由麦克斯韦创立的电磁学理论,和由爱因斯坦创立的狭义相对论.量子力学就大不相同了.为了得出它的数学方程式和意义解释,需要科学世界里最优秀的一批头脑的联合努力.不像在物理上已经得到充分发展和理解的经典力学那样,量子力学仍然在发展之中,并且仍然是在实验上和理论上都进行着紧张研究的一个领域.除了像定域性和测量问题之类为时已久的争论以外,量子现象的一些新领域仍然要进行探索和理解,例如量子传态(quantum teleportation),量子计算,包括玻色-爱因斯坦凝聚在内的宏观量子系统,多粒子纠缠态等等,依然不断地提出一些新的数学方程式以及新的解释,例如包括用正算符取值测度(positive-operator valued measures)和最大对称算符(maximal symmetric operators)去描述观察量,消相干(decoherence)和超选择定则(superselection rules)等等.近年出版的大量这方面的数学和哲学的专著以及教科书,反映了人们对于量子力学的强烈兴趣.
Here, we consider the Bell experiment for a system described by multipartite states in the case where ndichotomic observables are measured per site.If n is two, we consider a two-setting Bell experiment.If n is infinite, we consider an infinite-setting Bell experiment.Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment.Infinite-setting model is an explicit local realistic model for the values of a correlation function, given in an infinite-setting Bell experiment.In the non-contextual scenario, there is not the essential difference between infinite-setting model and two-setting model.And we cannot classify local realistic theories in this case.This says that we can construct infinite-setting model from two-setting model.Surprisingly we can discuss incompleteness in the Bell theorem by using non-contextual models.On the other hand, in the contextual scenario, there is the essential difference between infinite-setting model and two-setting model.This says that we must distinguish infinite-setting model from two-setting model.And we can classify local realistic theories in this case.
Malley and Fine (Phys. Rev. A 2006 73 066102) discussed that all quantum observables would commute simultaneously if we accept a realistic theory of the Bell type (a local realistic theory) for quantum events, provided that all quantum events, including every quantum state and every observable (including every projector), are reproduced by a realistic theory of the Bell type for quantum events. We point out that their claim leads us to a contradiction. We study the relation between a local realistic theory and commutativity of quantum observables in a finite-dimensional space. We show that a realistic theory of the Bell type for quantum events does not impose the commutative algebraic structure into the set of all quantum observables if all quantum events are reproduced by a local realistic theory. We discuss that a violation of Bell locality is derived within a realistic theory of the Kochen?Specker type within quantum events.
Quantum拓扑,一种量子力学中存在的奇特结构,为量子计算提供了独特的优势。本研究提出了一种基于量子拓扑的自适应量子计算量子路径优化方法,旨在利用拓扑结构优化量子路径,从而提高计算效率。该方法借鉴了量子拓扑的特性,通过构建拓扑结构来指导量子路径的优化,从而实现更高效的量子计算。该方法具有自动学习能力,并能够针对不同问题优化量子路径,为量子计算的发展提供新的思路。