量子纠缠和贝尔不等式及其在量子信息处理中的应用

1964年,爱尔兰数学家约翰·贝尔(John Bell)根据隐变量理论推导出了2个粒子系统的测量结果应该满足的不等式关系和所涉及的测量基本逻辑.法国科学家阿兰·阿斯佩(Alain Aspect)、美国科学家约翰·克劳泽(John Clauser)和奥地利科学家安东·蔡林格(Anton Zeilinger)分别从实验上证伪了该不等式.贝尔不等式的证伪宣告了隐变量理论的终结,展示了量子纠缠的奇特性质.为表彰他们在“纠缠光子实验、验证违反贝尔不等式和开创量子信息科学”方面所做出的贡献,瑞典皇家科学院将2022年诺贝尔物理学奖授予这3位科学家.本文概述了量子纠缠的概念和贝尔不等式的推导,介绍了2022年诺贝尔物理学奖获得者的代表性研究工作,并展示了量子技术的可能应用.     

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光子的先驱性实验,李政道和杨振宁关于产生两个中性K介子K⁰—${\\rm{\\bar K}}$⁰形成EPR态的建议,史砚华、欧泽宇、彭堃墀等利用非线性光学晶体,包括陈创天等人发现的非线性光学晶体,产生纠缠光子对的原创性工作。     

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.     

量子信息与计算

量子信息与计算是物理学目前研究的热门领域,本文简要地介绍量子计算的一些基本概念：量子纠缠、量子位、量子寄存器、量子并行计算和量子纠错,并介绍两种典型的量子信息技术：量子密码和量子传物。     

量子理论若干基本问题研究的新进展

本结合最后的典型量子物理实验,如用冷原子Bragg散射实现的“which-way”实验,量子退相干过程的微腔QED检验和C60分子的量子干涉等,比较系统地介绍了量子理论基本问题若干研究的新进展,特别强调了处于其核心的量子测量问题及其相关的基本概念和基本思想,如EPR佯谬和Bell不等式,量子退相干和量子纠缠,从理论和实验结合的角度本阐述了被测系统和测量仪器的相互作用怎样导致量子测量的一般动力学过程,由此还讨论了外部环境和内部运动怎样诱导量子退相干和量子耗散,对“薛定谔猫佯谬”和“宏观物体空间局域化描述”给出了可能的物理解释,最后,通过具体例子,本简单地讨论了量子物理基本问题的研究结果对量子信息的应用。     

量子信息讲座 第六讲 量子隐形传态

量子隐形传态是一个新颖和有趣的研究课题。它是量子力学奇妙特性的一种应用。文章阐述了量子隐形传态的基本原理,以及ＥＰＲ效应,Ｂｅｌｌ基测量等相关的概念,并介绍了基于量子光学技术而实现的两个量子隐形传态的成功实验。     

2022年诺贝尔物理学奖的科学内涵辨识

2022年的诺贝尔物理学奖,被一些人误解为证明了量子纠缠现象。实际上,包括爱因斯坦本人都承认量子纠缠,关键在于如何诠释。今年诺贝尔物理学奖的价值在于这几位物理学家以无可争辩的实验事实,证明了基于定域隐变量的贝尔不等式是不对的。目前的一些介绍文字,没有认真解释量子力学在理论上是如何批驳贝尔不等式的,同时虽对量子纠缠的物理价值多有阐述,但对其哲学意义却鲜有评述,对社会上滥用纠缠概念缺少直接批判和阐释。文章希望在这两方面有所补充。     

量子力学佯谬及第二次量子革命

文章介绍了三个著名的量子力学佯谬,分别是有关量子力学与定域实在性、语境实在性,以及宏观实在性三者之间的关系。这三个佯谬对应三个思想实验,后来又发展出由隐变量理论和实在性推导出的不等式,这些不等式可以定量地判断量子力学和这些实在性之间的关系,使得纠缠等量子力学特性成为可以被真实探测和利用的资源,被广泛应用于量子保密通信、量子隐形传态、量子计算等任务中。量子信息理论的出现,进一步带动了量子通信、量子计算和量子传感等高新技术领域的产生和发展,开启了“第二次量子革命”     

量子物理百年历程

 20世纪科学史册中最有影响的科学进展大概应当包括广义相对论、量子力学、大爆炸宇宙学、遗传密码的破译、进化生物学以及读者选择的其他一些课题。在这些进展当中,量子力学因其深奥的根本属性,而具有更加独特的地位。     

最子信息讲座续讲第五讲 关于连续变量的量子隐形传态

介绍了通过双模压缩真空态实现连续变量量子隐形传态的方法,并探讨了这一工作的重要意义及其相对于分离变量量子隐形传态的优越性。     

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.     

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.     

Comparison between local Kolmogorovian models and Bell's inequality

The conditions on the relative frequencies of coincidence between the measurements on two physical systems are deduced, in the particular case of four different directions, from Kolmogorovian probability and the Gutkowski and Valdes-Franco computational method. These conditions are compared with those imposed by Bell's inequality. It is proved that Bell's inequality is a necessary but not a sufficient condition for local Kolmogorovian probability. The further assumptions to be added to Bell's inequality, in order to prove the equivalence with local Kolmogorovian probability, are studied. The connection with the results obtained by other authors on the subject is discussed.     

Entanglement in 2DEG systems: towards a detection loophole-free test of Bell's inequality

We make use of the intrinsic noiseless and lossless aspect of an electron source in a 2DEG system to implement a new test of Bell's inequality. The generated entanglement can be tested by two-particle interferometry. Preparation and detection schemes of two complete sets of Bell states are given. A novel type of Bell's inequality is then derived in terms of noise correlation measurements. The characteristics of the electron source are essential to exhibit a violation. This electron system could close the detection efficiency loophole.     

Efficient scheme for entangled states and quantum information transfer with trapped atoms in a resonator

A protocol is proposed to generate atomic entangled states and implement quantum information transfer in a cavity quantum electrodynamics system. It utilizes Raman transitions or stimulated Raman adiabatic passages between two systems to entangle the ground states of two three-state Λ-type atoms trapped in a single mode cavity. It does not need the measurements on cavity field nor atomic detection and can be implemented in a deterministic fashion. Since the present protocol is insensitive to both cavity decay and atomic spontaneous emission, it may have some interesting applications in quantum information processing.     

原子偶极压缩的相干控制和Cauchy-Schwarz不等式的破坏

通过研究孤立二能级原子与双模纠缠相干光场的相互作用,分析了体系中原子偶极压缩量子效应的时间演化规律.体系中作用场模的性质决定了原子偶极压缩程度;同时定义了体系的Cauchy-Schwarz不等式破坏参数ΔV,研究了不同条件下参数ΔV的时间演化特性,Cauchy-Schwarz不等式破坏程度和体系中所具有的非经典特性是一致的;即可以通过调控相干场参数来远程控制体系中的非经典特性. 关键词： 量子光学 双模纠缠相干态 偶极压缩效应 Cauchy-Schwarz 不等式     

三光子GHZ态中不同Bell型不等式的实验研究

实验研究了Bell不等式、Mermin不等式和Svetlichny不等式在GHZ态中对定域实在论结果的破坏. 采用目标态密度矩阵的方法给出了实验制备的GHZ态的保真度, 得到了三个不等式在GHZ态中的测量值. 实验结果表明, 三个Bell型不等式在同一个状态下对定域实在论结果破坏程度不同, 在量子密钥分配中可以选择合适的非定域性描述方式考察所用信道的安全性.     

Preparation of multipartite entangled states used for quantum information networks

The preparation of multipartite entangled states is the prerequisite for exploring quantum information networks and quantum computation.In this paper,we review the experimental progress in the preparation of cluster states and multi-color entangled states with continuous variables.The preparation of lager scale multipartite entangled state provide valuable quantum resources to implement more complex quantum informational tasks.     

Multiparty quantum secret conference based on quantum encryption with pure entangled states

We present a scheme for multiparty quantum remote secret conference (MQRSC) with pure entangled states, not maximally entangled multipartite quantum systems. The conferees first share a private quantum key, a sequence of pure entangled states and then use them to encode and decode the secret messages. The conferees exploit the decoy-photon technique to ensure the security of the transmission of qubits. This MQRSC scheme is more feasible and efficient than others.     

A careful estimation of photon rescatterig in atomic-cascade experimental tests of Bell's inequality

Summary In this paper we show that, in every atomic-cascade experiment performed up to now for testing Bell's inequality, the second photon of the atomic cascade undergoes rescattering with considerable probability. The only experiment of this type in which rescattering is negligible is the Holt and Pipkin's one, but this is also the only experiment whose results grossly violate quantum-mechanical predictions.

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Riassunto Nel presente lavoro si mostra che, in ogni esperimento con cascata atomica realizzato fino ad oggi per indagare la disuguaglianza di Bell, la probabilità che il secondo fotone della cascata atomica subisca rescattering è notevolumente alta. L'unico esperimento del tipo suddetto in cui il rescattering è trascurabile è quello di Holt e Pipkin, ma questo è anche l'unico esperimento i cui risultati sono in netto contrasto con le previsioni quantomeccaniche.

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Резюме В этой статье мы показываем, что в экспериментах по наблюдению атомных каскадов, вьшолненных для проверки неравенства Белла, второй фотон атомного каскада претерпевает перерассеяние с большой вероятностью. Единственный эксперимент этого типа, в котором процесс перерассеяния пренебрежимо мал, является эксперимент Хольта и Пипкина. Но указанный эксперимент, в свою очередь, является единственным экспериментом, результаты которого существенно противоречат предсказаниям квантовой межаники.