贝尔不等式的量子违背及其实验检验——兼议2022年诺贝尔物理学奖

2022年诺贝尔物理学奖授予法国、美国和奥地利的三位科学家阿兰·阿斯佩、约翰·弗朗西斯·克劳泽和安东·塞林格,以表彰他们利用纠缠光子实验检验贝尔不等式以及在开拓量子信息科学方面做出的卓越贡献。贝尔不等式在量子力学基本问题和量子信息研究中都有着不可或缺的地位,它的违背直接揭示了量子力学的基本特征——量子非定域性。文章在讲清楚基本科学概念的基础上,简要介绍了贝尔不等式理论的建立及验证其违背的实验研究的科学历程。为了解决EPR佯谬,基于玻姆的定域隐变量理论,约翰·贝尔提出了关于纠缠态上的关联测量满足的基本不等式——贝尔不等式。他还发现,量子力学关于关联的计算结果违背贝尔不等式,可以在类空距离上展现出“鬼魅”的长程量子关联。这种长程关联看似有超光速的“超距作用”,但这只是人们明显或潜在地使用了“波包塌缩假设”。EPR文章明显地采用这个假设推断远方客体共存的物理实在要素,由此对量子力学完备性提出质疑。文章评述了阿斯佩、克劳泽和塞林格荣获诺贝尔物理学奖的关于贝尔不等式违背的判定性实验,介绍了华人物理学家在纠缠态和贝尔不等式研究方面的基础性贡献,包括早年吴健雄利用正负电子湮灭产生EPR光子的先驱性实...     

内禀退相干下Tavis-Cummings模型中原子的纠缠演化与贝尔不等式破坏

通过求解系统的Milburn方程，研究了两个二能级原子和单模场相互作用系统中原子间纠缠和贝尔不等式破坏随时间的演化特性，讨论了偶极相互作用、场与原子的失谐量对纠缠度以及贝尔不等式破坏的影响.结果表明：原子间偶极-偶极相互作用对纠缠度和贝尔不等式破坏有显著影响，失谐量增大会使两原子的纠缠度和贝尔不等式破坏变大，并且两原子所能达到稳定的纠缠受偶极相互作用系数与失谐量两者之差的影响.同时还发现两原子的纠缠与贝尔不等式破坏并不是单调的函数关系，很小的纠缠也可以产生贝尔不等式破坏. 关键词： Milburn理论 偶极-偶极相互作用 失谐量 贝尔不等式破坏     

基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

Aspect实验与两位科学巨人的争论--兼对批评的回答

指出Aspect实验同玻尔与爱因斯坦之间的巨人之争密切相关,阐述了玻姆思想实验与贝尔不等式的重要意义.     

Aspect实验与两位科学巨人的急论——兼对批评的回答

指出Aspect实验同玻尔与爱因斯坦之间的巨人之争密切相关,阐述了玻姆思想实验与贝尔不等式的重要意义。     

走近量子纠缠系列之六 纠缠态及实验

在谈到实验之前,还得顺便提一句,我们在此系列文章中,所谈到的量子纠缠以及推导贝尔不等式的过程,用的都是EPR佯谬简化了的波姆版。也就是说,我们使用了两个不同的自旋("上↑"和"下↓")来表述量子态,这使得问题叙述起来简化很多,因为在这种只有两个离散变量的情况下,单个粒子     

爱因斯坦与玻尔有关量子理论的旷世争论宣告终结

正三个关于贝尔不等式的实验测量,同时堵住了局域性漏洞和探测器漏洞。这些实验排除了最后的疑问,宣告了对局域唯实论彻底的放弃,同时也开启了通往新量子信息技术的大门。1935年,爱因斯坦(Albert Einstein)和Boris Podolsky、Nathan Rosen(EPR)三人写了一篇至今仍非常有名的文章,质疑了量子力学理论的完备性。他们不认为纠缠对中一个粒子的测量会影响远处另一个粒子的态,并认为:量子理论是不完备的,为了得到一个关于世界的合理的"局域唯实论"的描述,就必须补全量子理论的形式。他们认为一个粒子在局域范围内携带了其     

等距离耦合腔系统中的非局域性

本文研究的物理系统由3个二能级原子和3个等距离单模腔构成. 3个单模腔分别处于等边三角形的3个顶点, 腔与腔之间通过光纤耦合. 采用Mermin-Ardehali-Belinksii-Klyshko不等式(简称MABK不等式)表征三体量子态的非局域性. 本文利用数值计算方法, 研究了原子初态或腔场初态为W态情况下三体系统量子态的MABK不等式违背, 讨论了腔模与光纤模间的耦合系数变化对MABK不等式违背的影响. 计算结果表明: 三原子量子态和三腔场量子态均呈现出MABK不等式违背, 并且随腔模与光纤模间耦合系数增大, 三原子量子态的非局域性增强.     

基于奇偶校验门的非破坏性贝尔态测量

由于贝尔态测量是量子信息处理的前提,因此提出了一种针对贝尔态的非破坏性测量方案.在该方案中,将奇偶校验门作为关键器件,利用奇偶校验门不改变输入光子状态的特性实现了C-NOT门和Toffoli门.然后,将Toffoli门和Hadamard门结合实现了对4种贝尔态的确定性测量.所提方案可用于双光子纠缠态测量,并可推广到三光子纠缠态的应用场景中,为贝尔态测量与量子信息处理提供了新的思路.     

规范场和夸克动力学模型--关于QCD和层子模型的议论

文章讨论了夸克QCD模型和层子模型的关系，说明夸克动力学模型的基础是非亚贝尔规范场理论．层子模型是半唯象理论，没有动力学互作用的机制．QCD由于以非亚贝尔规范场为动力学互作用机制，在高能行为有渐近自由的重要性质．层子模型是低能束缚态的唯象性质的模型，与渐近自由是完全无关．强调“渐近自由”是一个独立于夸克模型的物理概念，它的理论基础是非亚贝尔规范场理论；当把非亚贝尔规范场作为夸克相互作用建立了夸克的动力学模型——量子色动力学（quantum chromodynamics，QCD）；层子模型是想把静态夸克模型发展为动力学模型，但它走的路线与QCD完全不同，层子的互作用不涉及非亚贝尔规范场，与渐近自由是不同概念和不同思想和不同考察区域；文章还指出夸克动力学的QCD模型同层子模型是哲学思想不同，物理思想也不相同的路线，层子模型没有接纳非亚贝尔规范场而未能达成创新的成果．文章也强调三十多年前层子模型研究的创新意识和团队精神是我们值得推崇的优秀传统．     

Violations of Bell's Inequality in Synchronized Hyperchaos

Motivated by a parallel between quantum cryptography and chaos synchronization cryptography, we construct a Bell's inequality for a pair of synchronously coupled variable-order Generalized Rossler Systems, with arbitrarily binarized final states. In the infinite-order limit, although dynamical parameters cannot be extracted from the coupling signal in finite time, the inequality is violated, as with entangled quantum states. The violations are weaker than in quantum theory, vanishing as the differences between corresponding parameters of the coupled systems become small. The fact that Bell's inequality can be violated for a pair of classical systems that are not discernibly connected supports the possibility of a realist interpretation of quantum mechanics.     

Interpretation of the Experiments on Bell's Inequality

The conceptual scheme of the optical polarization experiments on Bell's inequality is discussed. By invoking the distinction between the concepts of state preparation and measumment in quantum mechanics, it is argued that Bell's theorem is not applicable to this class of experiments in the way it is generally done. Consequently, by considering the specific features of the measurements performed hitherto, it is also shown that a local approach can yield the same theoretical prediction as the nonlocal quantum interpretation, even in the absence of other experimental loopholes.     

Violation of Locality Beyond Bell's Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Bell-type joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.     

About a Generalization of Bell's Inequality

We make use of natural induction to propose, following John Ju Sakurai, a generalization of Bell's inequality for two spin s=n/2(n=1,2,...) particle systems in a singlet state. We have found that for any finite integer or half-integer spin Bell's inequality is violated when the terms in the inequality are calculated from a quantum mechanical point of view. In the final expression for this inequality the two members therein are expressed in terms of a single parameter . Violation occurs for in some interval of the form (,/2) where parameter becomes closer and closer to /2, as the spin grows, that is, the greater the spin number the size of the interval in which violation occurs diminishes to zero. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the non-local point of view of orthodox quantum mechanics. So our conclusion may also be stated by saying that for large spin numbers the non-local and local points of view agree.     

Stronger-Than-Quantum Correlations

After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.     

The geometry of violation of Bell''''s inequality

The purpose of this paper is to deduce an analytical expression for the violation of Bell's inequality by quantum theory and plane trigonometry, and expound the violation and maximal violation of the first, second type Bell's inequality in detail. Further, we find out the sufficient conditions for the region in which Bell's inequalities are violated.     

Quantum Nonlocality and Generation of Multi-mode Schrodinger Cat States

We describe the Greenberger-Horne-Zeilinger (GHZ) paradox in the multi-mode Schroedinger cat states.We also show that the multi-mode cat states violate the Bell‘s inequality by an amount that grows exponentially with number of modes. The test of quantum nonlocality is based on parity measurement and displacement operation, which are experimentally feasible. We also describe a scheme for the generation of the cat states in cavity QED.     

Bell's inequalities and quantum communication complexity

We prove that for every Bell's inequality, including those which are not yet known, there always exists a communication complexity problem, for which a protocol assisted by states which violate the inequality is more efficient than any classical protocol. Violation of Bell's inequalities is the necessary and sufficient condition for quantum protocol to beat the classical ones.     

Photon entanglement in the phase-space Q representation of quantum optics

Several examples of photon entanglement are studied in the Q representation of quantum optics. In particular, the entangled states produced in parametric downconversion are studied in detail, and we determine the conditions for the violation of Bell's inequality. Our approach shows that photon entanglement is related to the existence of correlations between the quantum fluctuations of the electromagnetic field associated to different modes. Received 10 August 2002 / Received in final form 7 November 2002 Published online 4 February 2003     

Criticizing Bell: Local realism and quantum physics reconciled

A typical sample of Bell's inequality is proved to require, besides the standard assumptions on realism and locality, the adoption of a metatheoretical classical principle for interpreting quantum laws. A new principle is proposed which is consistent with the operational philosophy of quantum physics; it is then shown that, whenever the latter principle is adopted in place of the former, realism (here intended in a purely semantical sense) and locality do not imply Bell's inequality in the form considered here, but a new inequality which is not violated in quantum physics. Thus an interpretation of quantum physics that is (semantically) realistic and local is suggested, which eliminates a number of seeming paradoxes.