Nonlocality of Hardy type in experiments using independent particle sources
Xu-Bo Zou, Hai-Woong Lee, Jaewan Kim, Jae-Weon Lee, Eok Kyun Lee
通过应用哈代的论点，我们证明了在一个gedanken实验中使用独立的和分离的粒子源的局部现实主义的违反。
By applying Hardy's argument, we demonstrate the violation of local realism in a gedanken experiment using independent and separated particle sources.
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Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.
Hardy-type nonlocality proof for two maximally entangled particles
我们提出了一个变化的gedanken实验的哈代[物理学评论快报。68（1992）2981]首次给出了四维希尔伯特空间中两个最大纠缠粒子的Hardy型非定域性证明。
Do Hardy-type proposals test nonlocality of single-particle?
有人认为，哈代型的建议假设在检测非局部性，然后乞求的问题，或“本地空波”（本地隐藏变量），然后必须接受“许多世界”，不能证明非局部性。
Logical nonlocality is completely characterized by Hardy's "paradox" in (2,2,l) and (2,k,2) scenarios. We consider a variety of consequences and applications of this fact. (i) Polynomial algorithms may be given for deciding logical nonlocality in these scenarios. (ii) Bell states are the only entangled two-qubit states which are not logically nonlocal under projective measurements. (iii) It is possible to witness Hardy nonlocality with certainty in a simple tripartite quantum system. (iv) Noncommutativity of observables is necessary and sufficient for enabling logical nonlocality.
Revealing Incommensurability between Device-Independent Randomness, Nonlocality, and Entanglement using Hardy and Hardy-type Relations
在2-2-2场景下，本文利用Hardy和CLL非定域性关系全面处理了设备无关随机性量化，揭示了随机性、非定域性与纠缠间的定量不可通约性。
Hardy's nonlocality argument as witness for post-quantum correlation
最近，Gallego等人[Phys. Rev. Lett 107，210403（2011）]证明了任何旨在区分量子和后量子关联的未来信息原理本质上必须是多部分的。利用三量子系统的Hardy非定域性论证的器件无关成功概率，我们得到了类似的结果。我们构造了一个三部Hardy关联的例子，它是后量子的，但不仅满足所有二部信息原理，而且还满足GYNI不等式。
Persistence of Hardy's nonlocality in time
Hardy的非定域性论证证明了量子理论与定域实在论的不相容性，也可以用来揭示量子态的时间非定域性。对于自旋为1/2的系统，这个论证成功的最大概率是25%。我们表明，这个最大值保持25%的所有有限维量子系统与适当选择的观测。这使得测试的宏观系统的量子特性类似于莱格特和加格的方法。
Hardy's proof of nonlocality in the presence of noise
我们扩展的有效性，哈代的非局部性没有不等式证明，以涵盖的情况下，特殊的单参数类的非纯统计算子。这些混合态是通过将Hardy态与完全混沌噪声或色噪声混合而得到的，它们代表了非定域性实验中（纯）Hardy态的不完美制备过程的现实描述。在这样一个框架内，我们能够表现出一个精确的范围内的参数值测量噪声影响的非最佳准备的任意哈代状态，它仍然是可能的证据真正的非局部效应。同样，我们的工作表现出特定类别的二分混合态的成分不承认任何本地和确定性的隐变量模型再现量子力学的预测。
Local Orthogonality provides better upper bound for Hardy's nonlocality
在量子理论中，非定域性的数量与广义无信号理论[Found.Phys.24，379（1994）]中所允许的数量相比是有限的。例如，这一特征表现在贝尔不等式违反的数量以及哈代（Cabello）非定域性论证的成功概率程度上。在量子力学中，信息因果性和宏观定域性等物理原理被用来分析限制非定域性，即解释Cirel 'son限。然而，这些原则在解释量子理论中哈代和卡贝洛的最大成功概率时并不那么成功。在这里，我们表明，一个新提出的物理原理，即本地的非局域性做得更好，提供了一个更严格的上限上的成功概率为哈代的非局域性。与其他原理得到的边界相比，这个边界相对更接近于相应的量子值。
Hardy's nonlocality for generalized n-particle GHZ states
本文将Hardy关于两个自旋为1/2的粒子的非定域性证明[PRL 71（1993）1665]推广到n个自旋为1/2的粒子处于广义GHZ态的情况。我们发现，对于所有的n个\geq 3，任何纠缠的GHZ态违反贝尔不等式与哈代实验。这个特征是重要的，因为它已被证明[PRL 88（2002）210402]，对于所有n奇数，存在纠缠的GHZ态，不违反任何标准的n粒子相关贝尔不等式。
Hardy's criterion of nonlocality for mixed states
我们推广哈代的非定域性证明的情况下，二分混合统计算子，我们展示了一个必要条件，必须满足任何给定的混合状态$σ$，以便一个本地和现实的隐藏变量模型存在，占隐含的$σ$的量子力学预测。这个条件的失败将意味着不可能的任何局部解释某些联合概率分布的隐变量和不可分离的考虑混合统计算子。我们的结果也可以用来确定最大量的噪音，所产生的不完美的实验实现的原始哈代的证明的非局部性，在存在的情况下，它仍然是可能的证据投入到某些混合状态的非局部功能。
Chained Clauser-Horne-Shimony-Holt inequality for Hardy's ladder test of nonlocality
相对论因果关系禁止远距离观察者之间的超光速信号。利用非信号原理，我们导出了两个量子比特和每个量子比特K+1个可观测量的链式Clauser-Horne-Shimony-Holt相关和CHSH_K与Hardy阶梯非定域性检验成功概率P_K之间的精确关系。然后，通过调用CHSH_K的Tsirelson界，导出的关系允许我们建立P_K的上限。此外，我们还将CHSH_K与Clauser-Horne（CH）不等式的链式形式联系起来。
Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell's famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell's inequality. The alternative proofs of Bell's theorem without using Bell's inequality are known as `nonlocality without inequality (NLWI)' proofs. We, review one such proof, namely the Hardy's proof which due to its simplicity and generality has been considered the best version of Bell's theorem.
Testing Hardy nonlocality proof with genuine energy-time entanglement
我们给出了利用能量-时间关联光子进行量子非定域性Hardy阶梯检验的两种实验实现。Cabello \emph{et al.} [物理修订快报\textbf{102}，040401（2009）]。与以前的能量时间贝尔实验不同，这些测试需要精确定制的非最大纠缠态。其中之一是相当于两个设置两个结果贝尔测试需要一个最小的检测效率。所报道的实验仍然受到局部性和检测漏洞的影响，但没有以前的能量-时间和时间仓贝尔测试的后选择漏洞。
Nonlocality without inequality for almost all two-qubit entangled state based on Cabello's nonlocality argument
在这里，我们处理Cabello提出的非定域性参数比Hardy的非定域性参数更一般，但最大纠缠态不响应。然而，对于大多数其他纠缠态，这个论证的最大成功概率大于Hardy的论证。
NONLOCALITY OF A SINGLE PHOTON REVISITED AGAIN
评论L. Hardy，Phys. Rev. Lett. { \bf 73}，2279（1994）。认为哈代提出的实验不应被视为单光子实验。
Increased success probability in Hardy's nonlocality: Theory and demonstration
本文提出 n 粒子系统的哈代非局域性方案，结合解析模型与量子线路模拟，在真实量子计算机上验证，并证明成功概率渐近可达 15.6%，优于以往结果。
Hardy nonlocality for entangled pairs in a four-particle system
本研究探讨四粒子环状纠缠结构中Hardy非局域性的增强效应，通过量子电路模拟与实验验证，发现其相比完全纠缠系统具有更强的非局域性矛盾条件。
Maximum tri-partite Hardy's nonlocality respecting all bi-partite principles
遵守所有二部原理的多方相关性集合已被证明与时间有序双局部相关性集合相同。在此基础上，我们找到了在所有二分物理原理下三分Hardy关联成功概率的最大值。与量子力学不同的是，无信号原理并没有揭示出二体和三体系统的Hardy最大成功概率的任何缺口。信息因果原理成功地定性地揭示了这一量子特征，且这一结果与上述猜想无关。
Bell's inequality and extremal nonlocal box from Hardy's test for nonlocality
50年前，贝尔通过他著名的不等式证明了量子理论是非定域的，把量子非定域性问题从一个品味问题变成了一个测试问题。几年后，哈代提出了一个不带不等式的非定域性检验，这是一种“有与无”的论证。对$n$粒子的Hardy检验导致了一个$n$ -partite Bell不等式，其中每个观测者有两个二分的局部测量，所有纠缠纯态都违反了这个不等式。我们的第一个结果是表明，Bell-Hardy不等式所产生的Hardy的非定域性测试是严格的任意数量的缔约方，即，它定义了给定场景中贝尔多面体的一个面。另一方面，量子理论并不是非定域的，因为它禁止信号，甚至不像非信号条件所允许的那样非定域，即，量子力学预测形成所谓的非信号多面体的严格子集。在每个观察者测量两个二分观测量的场景中，弗里茨建立了贝尔多面体和非信号多面体之间的对偶性：紧贝尔不等式，贝尔多面体的面，与极端非信号盒一一对应，非信号多面体的顶点。我们的第二个结果是为这个对偶性提供一个替代的和更直接的公式。作为一个例子，紧Bell-Hardy不等式产生了一个极值非信号盒，它是Popescu-Rohrlich盒的自然多部推广。
Multipartite quantum states may exhibit different types of quantum entanglement in that they cannot be converted into each other by local quantum operations only, and fully understanding mathematical structures of different types of multipartite entanglement is a very challenging task. In this paper, from the viewpoint of Hardy's nonlocality, we compare W and GHZ states and show a couple of crucial different behaviors between them. Particularly, by developing a geometric model for the Hardy's nonlocality problem of W states, we derive an upper bound for its maximal violation probability, which…
Self-testing protocols enable certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in Bell experiment known as Hardy's test of nonlocality not only the maximally nonlocal correlation self-tests a quantum state, rather a non-maximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to self-test of every pure two qubit entangled state except the m…
Nonlocality tests of Bell Inequalities and of Hardy's "ladder theorem" without "supplementary assumptions"
我们已经通过实验测试了由高亮度纠缠源产生的状态的非局域性质，该纠缠源实际上允许直接测量由参量量子散射所暗示的基本QED过程所产生的全部光子对。标准贝尔测量和贝尔不等式违反测试已经实现了整个锥的发射的简并对。用同样的方法验证了Hardy阶梯理论的第20阶，并对41%的纠缠对验证了标准量子理论与局域实在论的矛盾。PACS：03.65.Ud，03.67.Mn，42.65.Lm
Quantum perfect correlations and Hardy's nonlocality theorem
本文讨论了Hardy关于最大纠缠态的非定域性证明的失败。详细的分析表明，这类态的Hardy方程的不相容性在物理上源于三对二值观测量的量子完美关联的存在（D_11，D_21），（D_11，D_22）和（D_12，D_21）[在确定性等于任何一对的联合测量的（不同）读数（D_11，D_21），（D_11，D_22），和（D_12，D_21）]，必然要求观测量对的完全相关（D_12，D_22）[在一定程度上具有对（D_12，D_22）的联合测量的相等（不同）读数的意义上]。实际上，这四个完美关联满足CHSH不等式，那么对于四个可观测量D_ij，i，j = 1，2，最大纠缠态将不会出现违反局域实在论的情况.这一事实和量子力学预言不可能给出最大可能的理论违反CHSH不等式之间的联系被指出。此外，它通常被证明，所有的Hardy非定域性条件的满足必然会导致违反所产生的CHSH不等式。最大的违反这后一个不等式是确定的。
Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states
我们证明了所有的$n$ -量子比特纠缠态，除了单量子比特和二体最大纠缠态的张量积，承认非局域性的Hardy型证明没有不等式或概率。更确切地说，我们表明，对于所有这样的状态，有本地的，单量子比特的可观测量，使得由此产生的概率表在阿布拉姆斯基和勃兰登堡的意义上是逻辑上下文，这是哈代型属性的一般形式。此外，我们的证明是建设性的：给定一个状态，我们展示了如何产生见证本地可观。事实上，我们给出了一个算法来做到这一点。虽然该算法相当简单，但其正确性的证明是不平凡的。另一个引人注目的特点是，我们表明，$n+2$本地可观的足以见证任何$n$ -量子位状态的逻辑上下文：两个每个两个为当事人，和一个每个为其余的$n-2$党。
Identification of all Hardy-type correlations for two photons or particles with spin 1/2
通过使用另一种等价形式的CHSH不等式，并广泛利用实验可检验的物理局域性的属性，我们确定了64个不同的贝尔型不等式（每一个涉及四个联合概率），其中哈代的非局部性定理可以铸造。这使得我们可以识别所有可以表现出哈代型非局域性的两量子比特相关性。
Hardy-type arguments manifest Bell nonlocality in one of the simplest possible ways. Except for demonstrating nonclassical signature of entangled states in question, they can also serve for device-independent self-testing of states, as shown, e.g., in Phys. Rev. Lett. 109, 180401 (2012). Here we develop and broaden these results to an extended version of Hardy's argument, often referred to as Cabello's nonlocality argument. We show that, as in the simpler case of Hardy's nonlocality argument, the maximum quantum value for Cabello's nonlocality is achieved by a pure two-qubit state and projecti…
Persistence of nonlocality for bipartite quantum spin systems
两个自旋为1（和自旋为3/2）的粒子的纠缠态的一般形式，以及一组适当的自旋观测值，一起表现出最大的非定域性下的哈代的非定域性测试给出;最大的非定域性被证明是0.09017。证明了这一结果对于两个自旋$j$粒子系统对所有的$j$值都是成立的。研究结果还表明，两个自旋$j$粒子的最大纠缠态对Hardy非定域性检验没有响应.
Bound on Hardy's non-locality from the principle of Information Causality
最近，信息因果关系的不违反原则[Nature 461，1101（2009）]已被提出作为自然的基本属性之一。我们探讨了两个量子比特系统的哈代非定域性定理，在广义概率论的背景下，信息因果关系的不违反原则的限制。应用，信息因果关系违反的充分条件，我们推导出一个上限的最大成功概率的哈代的非定域性参数。我们发现，这里达到的界限是高于量子力学所允许的，但仍然远远低于无信号条件所允许的。我们还研究了Cabello型非定域参数（广义哈代的论点）在这种情况下。
Almost all pure entangled states enable unbounded nonlocality sharing
研究在顺序二分场景中哈迪悖论与非定域性共享的联系，利用投影测量和局部辅助系统，几乎所有纯纠缠态（除最大纠缠态）能实现任意多对观察者间的非定域性共享。
Quantum Nonlocality Enhanced by Homogenization
在[Y.- C Wu和M. A 85，022119（2012）]是将具有偏相关的紧贝尔不等式变换成也是紧的全相关形式的过程。本文检验了两类$n$ -部贝尔不等式：Hardy不等式和紧贝尔不等式的无量子破坏的均匀化.对于Hardy不等式，其均匀化对最大纠缠态具有更强的量子破坏性;无量子破坏的紧贝尔不等式给出了量子和超量子的边界，但其均匀化不具有类似的性质.我们发现它们的均匀性被最大纠缠态破坏了。数值计算表明，广义GHZ态的均匀化Hardy不等式的量子破坏域比Hardy不等式的量子破坏域小。
A simple proof of the converse of Hardy's theorem
在本文中，我们提供了一个简单的证明，事实上，对于两个自旋为1/2的粒子系统，并选择的观测量，有一个独特的状态，显示哈代型非局域性。此外，一个明确的表达的概率，在这样的状态下准备的粒子对的合奏表现出哈代型非定域性矛盾的两个独立的参数有关的观测量。顺便说一句，一个错误的陈述表示在Mermin的证明的逆[N. D。梅尔明，美国J.Phys.62，880（1994）]中所指出的。
Nonlocality without inequalities has not been proved for maximally entangled states
两种方法来扩展的Hardy的非定域性证明没有不等式的最大纠缠态的二体两能级系统被证明是失败的。一方面，我们证明了吴和同事的证明[Phys.Rev.A53，R1927（1996）]使用了一个非最大纠缠的有效态。另一方面，它表明，哈代的证明不能被广义的四个冯诺依曼测量在原来的证明中所涉及的一个由一个广义的测量，以明确区分非正交状态的替代。
Self-testing of Nonmaximal Genuine Entangled States using Tripartite Hardy Relations
本文提出基于设置独立性和结果独立性的三体关联表征框架，证明三体Hardy非定域性比Mermin型不等式更强，能实现非极大真正纠缠态的自测试并生成最大约2.8073比特的与设备无关随机性。
Simple Hardy-like proof of quantum contextuality
上下文性和非定域性是自然界的两个基本属性。哈代的证明被认为是非定域性的最简单的证明，也可以被看作是对最简单的贝尔不等式的特殊违反。一个基本的问题是：哪一个是语境性的最简单证明？我们表明，有一个哈代一样的上下文证明，也可以被看作是一个特别违反最简单的noncontextuality不等式。有趣的是，这个新的证明将这个不等式与Kochen-Specker定理的证明联系起来，提供了这两个基本结果之间缺失的联系，并且可以扩展到任意奇数个$n$的设置，这种扩展可以被视为对$n$ -循环不等式的特殊违反。
Hardy-type self-testing and exposedness of tripartite GHZ correlations
研究三体两输入两输出场景中Hardy型悖论的自检验，证明最大Hardy成功概率关联自检验GHZ态和测量，且该关联是量子关联集的极点和暴露点，与Mermin不等式最大违反点重合。
Extreme nonlocality with one photon
量子非定域性通常被分配给两个或多个分离良好的粒子的系统，但非定域性也可以存在于仅由单个粒子组成的系统中，当人们认为子系统是遥远的空间场模式时。单粒子非定域性已通过二分贝尔不等式得到实验证实。本文给出了N个量子比特W态的局域实在论的一个贝尔不等式和一个N方Hardy证明.结果表明，在大N的限制下，Hardy类证明有效地变成了全对无（或GHZ类）证明，并且贝尔不等式的量子-经典能隙趋于与三粒子GHZ实验中的能隙相同.我们详细介绍了如何测试在现实系统中的非局域性。
The concept of quantum entanglement and hyper-entanglement, lying at the heart of quantum information science and technologies, is physically counter-intuitive and mathematically elusive. We design a polarization-encoded ghost imaging system based on the frame of Hardy nonlocality paradox to visualize the evidence of quantum hyper-entanglement by capturing purely nonlocal photonic events. In two-photon polarization-spatial-mode hyper-entangled state, spatial entanglement con-veys the ghost images while polarization entanglement encodes the imaging channels. Then whether imaging the single ghos…
Hardy's Paradox for High-Dimensional Systems: Beyond Hardy's Limit
哈代的证明被认为是非定域性的最简单的证明。在这里，我们介绍了一个同样简单的证明，（一）有哈代的作为一个特殊的情况下，（二）表明，非本地事件的概率增长与本地系统的尺寸，（三）总是相当于违反一个紧贝尔不等式。
We show that the Hardy nonlocality condition is equivalent to the violation of the CHSH inequality with additional constraints. We adapt the geometrical optimization of the violation of the CHSH inequality to these additional constraints and show that the Hardy condition is equivalent to optimizing the length difference of two sides in a triangle. Furthermore, we discuss the effects of the different constraints.
Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein, Podolsky and Rosen. These quantum correlations, now termed quantum nonlocality and tested by violation of Bell's inequality that consists of statistical correlations fulfilling local realism, have found loophole-free experimental confirmation. A more striking way to demonstrate the conflict exists, and can be extended to the multipartite scenario. Here we report experimental confirmation of…
Cabello's nonlocality argument for multisetting high-dimensional systems and its experimental test
本文提出一种新的多重设置高维非局域性论据框架，通过实验验证在(2,4)和(6,2)场景中非局域性概率分别达到20.29%和28.72%，超越传统非局域性界限。
Hardy-type experiment for the maximally entangled state: Illustrating the problem of subensemble postselection
通过选择一个特定的子系综的联合检测事件在一个两粒子干涉仪的安排，一个正式的非定域性矛盾的Hardy类型的粒子对配置在最大纠缠态的合奏。然而，有人认为，表现出这种矛盾的实验类并不排除局部实在论的假设。
Nonlocality without inequality for spin-s system
我们分析了哈代的非局部性参数为两个自旋-S系统，并表明，在这方面的早期解决方案是有限的，由于施加的一些条件，没有作用的非局部性参数。本文给出了两个自旋-s系统的非定域性条件的一个紧致形式，并将其推广到n个自旋-s粒子的情形。我们还将更一般的非定域性论证应用到更高自旋的系统中。
We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding …
In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
In this note, we study Cabello's nonlocality argument (CNA) for three-qubit systems configured in the generalized GHZ state. For this class of states, we show that CNA runs for almost all entangled ones, and that the maximum probability of success of CNA is 14% (approx.), which is attained for the maximally entangled GHZ state. This maximum probability is slightly higher than that achieved for the standard Hardy's nonlocality argument (HNA) for three qubits, namely 12.5%. Also, we show that the success probability of both HNA and CNA for three-qubit systems can reach a maximum of 50% in the fr…
Advantage of Hardy's Nonlocal Correlation in Reverse Zero-Error Channel Coding
本研究将Hardy非局域关联应用于双方通信，提出需Hardy非局域无信号关联辅助才能通过1比特通信获正收益的任务，证明反向零错误信道编码中非最大纠缠态可优于最大纠缠态，揭示纠缠资源结构的复杂性。
Ladder proof of nonlocality without inequalities and without probabilities
Hardy等人提出的两个自旋半粒子非定域性的无不等式梯形证明。79（1997）2755）只适用于非最大纠缠态，最多只适用于50%的纠缠对。给出了两个自旋为1的粒子处于最大纠缠态的一个类似的梯形证明。在最简单的形式中，证明通过了17%的对。扩展版本适用于100%的配对。证明可以扩展到两个自旋为s的粒子的任何最大纠缠态（s等于或大于1）。
Nonlocality of Symmetric States
本文研究了n比特置换对称态的非定域性质。我们将二分Hardy悖论和相关的CH-不等式推广到n方置换对称态，证明了所有对称态都具有非定域性。自然扩展的悖论和不平等的发展，涉及不同的纠缠类不同的非本地功能。我们定义了一个纠缠类的所有状态都违反的不等式，而该类之外的状态不违反。
Device-independent bounds for Hardy's experiment
在这封信中，我们计算一个类似的Tsirelson的限制为哈代的测试的非局部性，也就是说，最大限度地违反当地的限制所允许的量子形式主义，无论系统的尺寸。该值被发现是一个已经实现了与两个量子比特系统相同，我们表明，只有一个非常特定的类的状态可以导致这样的最大值，从而突出了哈迪的测试作为一个设备独立的自我测试协议，这样的状态。通过考虑现实的限制，在哈代的测试，我们还计算设备无关的上限，这种违反，并表明，这些界限是饱和的两个量子比特系统，从而表明，有没有优势，在使用高维系统在实验实现这样的测试。
Recently the authors in [Phys. Rev. Lett. 125, 090401 (2020)] considered the following scenario: Alice and Bob each have half of a pair of entangled qubit state. Bob measures his half and then passes his part to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice.…
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as "the simplest form of Bell's theorem". In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardy's paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit…
We show that any Bell local state, with a hidden nonlocality that can be revealed by local filtering, is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state, by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality, for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states, can be revealed by local operations and the sending of two one-bit messages, one in each…
The principle of non-violation of "information causality", has been proposed as one of the foundational properties of nature\cite{nature}. The main goal of the paper is to explore the gap between quantum mechanical correlations and those allowed by "information causality" in the context of local randomness by using Cabello's nonlocality argument. This is interesting because the gap is slightly different than in the context of Hardy's similar nonlocality argument\cite{gazi}
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, which successful implementation is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even nonlocal hidden variable models cannot reproduce the quantum predictions, allows for the device-indep…
Witnessing Genuine Mutipartite Non-locality
真正的多方非局域性是量子系统的一个显著特征，它赋予多方设备无关密码协议的安全性。在给定相关性的情况下，最近的研究已经对表征和检测非线性进行了研究。在这方面，我们提出了一个哈代型的论点，它能够检测到真正的$n$方式的非局域性的任意量子系统。为了理解这个论点的强度，我们还研究了最小约束理论中的论点的最佳成功概率，即广义无信号理论。
Entropic tests of multipartite nonlocality and state-independent contextuality
我们介绍了一个多部扩展的信息论距离首次介绍在[自然341，119（1989）]。我们使用这个新的距离来推导三个和任意偶数个量子比特的多体非定域性的熵测试以及与状态无关的上下文测试。此外，我们重新推导了Cabello [Phys. Rev. Lett. 101，210401（2008）]。这表明，信息论距离的方法，多部非局部性和状态独立的上下文可以提供一个更一般的处理非经典的相关性比正统的方法的基础上关联函数。
Single particle nonlocality with completely independent reference states
我们描述了一个计划，以证明一个单一的粒子的非局部性质，显示违反贝尔不等式。该方案是实验上可实现的，因为唯一的输入是数态和混合态，它们作为“跟踪实验”的参考。这些参考状态彼此完全独立地创建，并且仅在记录了所有测量结果之后才关联。这意味着任何观察到的非定域性必须完全是由于单粒子状态。所有使用的技术都同样适用于光子和大质量粒子，因此这个方案可以用来显示原子的非定域性。
We introduce, for any bipartite Bell scenario, a measure that quantifies both the amount of nonlocality and the efficiency in device-independent quantum key distribution of a set of measurement outcomes probabilities. It is a proper measure of nonlocality as it vanishes when this set is Bell local and does not increase under the allowed transformations of the nonlocality resource theory. This device-independent key rate $R$ is defined by optimizing over a class of protocols, to generate the raw keys, in which each legitimate party does not use just one preselected measurement but randomly choo…
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