Pure entangled states probed by multipartite Bell experiments
Jesús Urías
对Werner和Wolf提出的所有（n，2，2）Bell算子（在数量上为$2^{2^n}$，$n \ge 2$）进行谱分解.它的影响贝尔运营商的纠缠探针的表征被详细考虑。
The spectral decomposition of all (n,2,2) Bell operators ($2^{2^n}$ in number, $n \ge 2$), as introduced by Werner and Wolf, is done. Its implications on the characterization of Bell operators as probes of entanglement are considered in detail.
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Multipartite bound entangled states that violate Bell's inequality
本文研究了多体态的可量子化性与Bell不等式破坏之间的关系。我们证明了存在多体束缚纠缠态（即不可分、不可分离的纠缠态），它们违反了多体贝尔不等式.这意味着：（i）贝尔不等式的违反不是一个充分的条件，（ii）一些束缚纠缠态不能描述的本地隐变量模型。
Generic Bell inequalities for multipartite arbitrary dimensional systems
我们提出了多部多维系统的一般贝尔不等式。任何局域实在论都必须遵守的不等式被偶数维多体系统的量子力学所违背。一个大的变种集自然出现的通用贝尔不等式。我们讨论特殊的变种贝尔不等式，违反了所有的系统，包括奇维系统。
All tight multipartite Bell correlation inequalities for three dichotomic observables per observer
贝尔不等式的全套推导涉及关联函数，为双方，与二进制可观的，和三个可能的本地设置。该过程可以直接扩展到多方相关性。
We present a set of Bell inequalities for multiqubit quantum systems. These Bell inequalities are shown to be able to detect multiqubit entanglement better than previous Bell inequalities such as Werner-Wolf-Zukowski- Brukner ones. Computable formulas are presented for calculating the maximal violations of these Bell inequalities for any multiqubit states.
Multipartite omnidirectional generalized Bell inequality
我们推导出一个多部广义贝尔不等式，其中涉及到整个范围内的设置为每个本地观察员。特别地，它被应用于显示Greenberger-Horne-Zeilinger关联的六量子比特混合物的非定域行为比以前的贝尔不等式更强。对于某些噪声混合的相关性，一个明确的本地现实模型存在的情况下，一个标准的贝尔实验。贝尔实验与许多本地设置揭示了非局域性的状态。事实证明，在特定的量子态下，新的不等式比许多其他的贝尔不等式更加严格。
In this work, we present a new class of genuine multipartite Bell inequalities, that is particularly designed for multipartite device-independent (DI) quantum key distribution (QKD), also called DI conference key agreement. We prove the classical bounds of this inequality, discuss how to maximally violate it and show its usefulness by calculating achievable conference key rates via the violation of this Bell inequality. To this end, semidefinite programming techniques based on [Nat. Commun. 2, 238 (2011)] are employed and extended to the multipartite scenario. Our Bell inequality represents a …
Local measurements acting on entangled quantum states give rise to a rich correlation structure in the multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser-Horne-Shimony-Holt inequality, serves as the $seed$ to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feat…
A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A unified framework to establish all kinds of CHSH-type Bell inequalities by increasing step by step the number of observers is given. As an application, compact Bell inequalities, for eight observers, involving just four correlation functions are proposed. They require much less experimental effort than standard methods and thus is experimentally friendly in mul…
The problem of closing the detection loophole in Bell tests is investigated in the presence of a limited number of efficient detectors using emblematic multipartite quantum states. To this end, a family of multipartite Bell inequalities is introduced basing on local projective measurements conducted by $N-k$ parties and applying a $k$-party Bell inequality on the remaining parties. Surprisingly, we find that most of the studied pure multipartite states involving e.g. cluster states, the Dicke states, and the Greenberger-Horne-Zeilinger states can violate our inequalities with only the use of t…
Return operator, cross Bell bases and protocol of teleportation of arbitrary multipartite qubit entanglement
本文定义了返回算子、叉积算子和叉Bell基。利用交叉Bell基，我们给出了一个任意多体量子比特纠缠态的隐形传态协议，该方案是BBCJPW方案的一个很自然的推广。我们发现，这种隐形传态实际上是由每个未知量子比特态的隐形传态决定的，就像BBCJPW的原始方案一样。对于三分量子比特的情况，给出了详细的计算。
Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios
本研究提出基于多体Bell场景非信号多胞体的经典模拟算法，可模拟通用测量型量子计算，明确量子加速的必要条件，拓展了可高效模拟的量子态范围。
We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by GHZ states, and vice versa. Next, we devise 'sub-correlation Bell inequalities' for any number of parties, which can provably…
Superactivation of genuine multipartite Bell nonlocality from two-party entanglement
研究揭示了通过双体纠缠在多复制情况下实现真正的多体非局域性的最弱资源，提出了一种高效的认证方法和完美并行重复结果。
Optimizing quantum violation for multipartite facet Bell inequalities
本文提出基于梯度的方法优化多体Bell不等式，以提高其量子违反程度，从而更有效地研究多体非局部性。
Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property for multipartite states and actually there are not many known candidates. In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states, with two observables for each local party. We show that the constructed Bell inequalities can self-test any stabilizer state whi…
Tight multipartite Bell's inequalities involving many measurement settings
我们得到了N>2个观测者的紧Bell不等式，其中包含两个以上的测量设置。我们给出了一般量子态违反新不等式的一个充要条件。的不等式被违反的一些类的状态，其中所有标准的贝尔不等式与每个观察员两个测量设置是满意的。
Tight Correlation-Function Bell Inequality for Multipartite $d$-Dimensional System
将Clauser-Horne-Shimony-Holt（CHSH）不等式的关联函数推广到多体d维系统.基于此推广的所有贝尔不等式都具有与CHSH不等式相同的简单形式。对于小系统，数值结果表明新的不等式是紧的，我们相信这也适用于高维系统。此外，新的不等式与以前的不等式是相关的，对于二部系统，我们的不等式等价于Collins-Gisin-Linden-Masser-Popescu（CGLMP）不等式.
We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second we analyze GHZ states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments rep…
We present a set of Bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions. The relations between Bell inequalities and distillability are also studied. We show that any quantum states that violate one of these Bell inequalities are distillable.
Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making their experimental implementation difficult. The main purpose of this work is to explore the possibility of witnessing nonlocality in multipartite quantum states from the easiest-to-measure quantities, that is, the two-body correlations. In particular, we determine all three and four-partite Bell inequalities constructed from one and two-body expectation val…
Quantum correlations arising in Bell experiments, involving a physical source that emits a quantum state to a number of observers, have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond the Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments c…
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many …
We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also ob…
Wigner's argument inferring Bell-type inequality for the EPR-Bohm entangled state is generalized here for any N-partite state. This is based on assuming for the relevant dichotomic observables the existence of the overall joint probability distributions, satisfying the locality condition, that would yield the measurable marginal probabilities. For any N, such Generalized Wigner's Inequality (GWI) is violated by quantum mechanics for all pure entangled states. The efficacy of GWI is probed, comparing with the Seevinck-Svetlichny multipartite Bell-type inequality, by calculating threshold visibi…
The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions appreh…
Quadratic Bell inequalities as tests for multipartite entanglement
这封信提出了量子力学不等式，区分，为系统的$N$自旋$\half$粒子（$N>2$），完全纠缠态和状态，其中最多$N-1$粒子纠缠。这些不等式比Gisin和Bechmann-Pasquinucci [Phys.\ Lett. A { \bf 246}，1（1998）]和Seevinck和Svetlichny [quant-ph/0201046]。
A simple scheme of teleportation of arbitrary multipartite qubit entanglement
本文定义了一个叉积算符，构造了一个叉Bell基，利用这个基和Bell测量，给出了一个简单的任意多体量子比特纠缠态的隐形传送方案。
We investigate the problem of closing the detection loophole in multipartite Bell tests, and show that the required detection efficiencies can be significantly lowered compared to the bipartite case. In particular, we present Bell tests based on n-qubit Greenberger-Horne-Zeilinger states, which can tolerate efficiencies as low as 38% for a reasonable number of parties and measurements. Even in the presence of a significant amount of noise, efficiencies below 50% can be tolerated, which is encouraging given recent experimental progress. Finally we give strong evidence that, for a sufficiently l…
We show that violation of genuine multipartite Bell inequalities can be obtained with sampled, probabilistic phase space methods. These genuine Bell violations cannot be replicated if any part of the system is described by a local hidden variable theory. The Bell violations are simulated probabilistically using quantum phase-space representations. We treat mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60 qubits, using both a multipartite SU(2) Q-representation and the positive P-representation. Surprisingly, we find that sampling with phase-space distributions can …
We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust violations of local causality than obtained previously. We analytically calculate the optimal function and include the effect of nonideal detectors and noise, revealing that optimized functional inequalities are resistant to standard forms of decoherence. These inequalities could allow a loophole-free Bell test with efficient homodyne detection.
In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements…
For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some conditions on the local dimension the probability to find any significant amount of violation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that if the number of parts is at least 3, this probability also goes to zero as the the local Hilbert space dimension goes to infinity.
Detecting Bell correlations in multipartite non-Gaussian spin states
本研究引入含少体关联子的置换不变Bell不等式（PIBI）拓展多体系统Bell关联研究工具，提出适用于任意粒子数的多族PIBI，具备更高噪声鲁棒性或非高斯自旋态Bell关联探测能力，并通过半定规划寻找可实验实现的PIBI。
Dür [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $N\ge 8$, and his result was recently improved by showing that there exists an $N$-qubit bound entangled state violating the Bell inequality if and only if $N\ge 6$ [Phys. Rev. A {\bf 79}, 032309 (2009)]. On the other hand, it has been also shown that the states which Dür considered violate Bell inequalities different from the inequality for $N\ge 6$. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities …
All tight multipartite Bell correlation inequalities for an arbitrary number of dichotomic observables per observer
推导出包含关联函数的贝尔不等式的完整集合，对于两方，具有二进制可观测量和N个可能的局部设置，并不像看起来那么容易。v1的证明是错误的。此外，我们还可以找到一个反例，很快就会提出来。因此，我们的论文是死的。手稿（v1）中讨论的一系列贝尔不等式仍然是局部实在论的必要条件，而且是紧的。它们仅在每个观察者N=3的情况下是紧密和完整的（足够的）（如quant-ph/0611086所示，幸运的是使用了完全不同的方法）。
Better detection of Multipartite Bound Entanglement with Three-Setting Bell Inequalities
它发表在物理评论快报上，87，230402（2001）证明了由某个单参数束缚纠缠态族F描述的N（N ≥ 4）个量子比特在N ≥ 8时违反Mermin-Klyshko不等式。在本文中，我们证明了来自家庭F的状态违反贝尔不等式在物理Rev.A，56，R1682（1997），其中每个观察者测量三个非交换集的正交投影，N >=7。我们还导出了一个简单的单参数纠缠见证族，它可以检测所有属于F的态的纠缠。这些新的纠缠见证可能是由某些贝尔不等式产生的。
An elegant proof of self-testing for multipartite Bell inequalities
本工作提出了一种简单且广泛适用的自测试论证，用于N体关联贝尔不等式，推广了Mayer-Yao公式并突破了线性不等式限制，为MABK、WWWŻB和Uffink不等式族提供了自测试证明。
Configuration of separability and tests for multipartite entanglement in Bell-type experiments
在任意维空间上，我们得到了各种混合可分-不可分$n$ -粒子密度算子的紧二次不等式。这种方法使我们能够真正推导出一个紧二次不等式，作为在各种Bell型相关实验中对完全$n$ -partite纠缠的测试，这些实验可能不被识别为量子比特的集合，例如，那些涉及由不完整的探测器测量的光子。当两个观测量精确对易时，一个更强的二次不等式可以证明$n$ -体纠缠。
All multipartite Bell correlation inequalities for two dichotomic observables per site
本文对具有两个二分观测量的n部系统构造了一组2^（2^n）个独立的Bell相关不等式，当且仅当所考虑的相关允许局部经典模型时，这组不等式是完备的.所有这些不等式都可以归纳为一个非线性不等式。我们表明，量子关联满足这个条件，提供的状态有正的部分转置相对于任何分组的n个系统成两个子系统。我们还提供了一个有效的算法来寻找每个不等式的最大量子力学破坏，并表明，最大值总是达到广义GHZ状态。
Multipartite entanglement measures via Bell basis measurements
本文提出利用贝尔基测量数据估计多体纠缠度量的新方案，重点扩展Concentratable Entanglements至混合态并构造可估计下界，同时降低实验要求并简化重复次数分析，最终在里德伯原子量子计算机模拟中验证了可行性。
Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomo…
Tight and self-testing multipartite quantum Bell inequalities from the renormalization group
该研究提出紧致连接器概念，构造出随N指数提升量子-经典值比的N体量子贝尔不等式，其生成的不等式具紧致性与完全自检验特性。
Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement dept…
Recently, it was demonstrated by Son et al., Phys. Rev. Lett. \textbf{102}, 110404 (2009), that a separable bipartite continuous variable quantum system can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality via operationally local transformations. Operationally local transformations are parameterized only by local variables, however in order to allow violation of the CHSH inequality a maximally entangled ancilla was necessary. The use of the entangled ancilla in this scheme caused the state under test to become dependent on the measurement choice one uses to calculate the CHSH inequalit…
We estimate the probability of random $N$-qudit pure states violating full-correlation Bell inequalities with two dichotomic observables per site. These inequalities can show violations that grow exponentially with $N$, but we prove this is not the typical case. For many-qubit states the probability to violate any of these inequalities by an amount that grows linearly with $N$ is vanishingly small. If each system's Hilbert space dimension is larger than two, on the other hand, the probability of seeing \emph{any} violation is already small. For the qubits case we discuss furthermore the conseq…
Optimizing and Certifying Multipartite Permutationally Invariant Bell Inequalities
研究多体贝尔非定域性表征受限问题，开发用单双粒子关联器构建和验证置换不变贝尔不等式的可扩展方法，优化量子值与经典界限比率，通过集体测量有效检测多体贝尔非定域性。
A resource- and computationally-efficient protocol for multipartite entanglement distribution in Bell-pair networks
研究从贝尔对网络生成多方纠缠态（如GHZ态）的协议，提出计算高效协议，其门数需求、时间复杂度及贝尔对消耗接近最优，优于基于斯坦纳树的协议，还分析了噪声对GHZ态保真度的影响。
Size-Independent Robustness in Multipartite Bell Self-Testing
该研究解决多体纠缠自测试受系统规模限制的问题，推导n量子比特GHZ态的设备无关自测试界，实现任意大系统中固定噪声下的GHZ纠缠认证，支持可扩展设备无关验证。
The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elu…
Experimental certification of multipartite Bell correlations using only few-body symmetric correlations
本研究证明利用少体置换不变关联即可认证多体贝尔关联，通过六、八光子Dicke态实验验证，显著提升噪声容忍度，为大型系统提供无需全体系测量的可行认证方案。
Refined Tsirelson Bounds on Multipartite Bell Inequalities
针对多方量子关联刻画难题，本文利用类似量子不确定性的基本约束，推导依赖子系统关联的 Svetlichny 与 MK 不等式精细化 Tsirelson 界，并通过实例证明其更紧。
The structure of Bell-type inequalities detecting genuine multipartite non-locality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite non-locality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally we discuss the thightness and quantum me…
While Bell nonlocality of a bipartite system is counter-intuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrati…
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 …
Variants of Bell inequalities
本文给出了一类Bell型不等式，它是由每个点包含两个二分观测量的“标准”贝尔不等式直接构造的.结果表明，多量子比特的广义Greenberger-Horne-Zeilinger态都不满足上述不等式.值得注意的是，我们的新的不等式可以提供更强的非局部性测试在某种意义上说，当地的现实不平等指数强于相应的多部可分性不等式。这表明，可分态对定域实在论的指数破坏是多体系统量子涨落的一个有趣结果。
We propose two semi-device-independent approaches that are able to quantify unknown multipartite quantum entanglement experimentally, where the only information that has to be known beforehand is quantum dimension, and the concept that plays a key role is nondegenerate Bell inequalities. Specifically, using the nondegeneracy of multipartite Bell inequalities, we obtain useful information on the purity of target quantum state. Combined with an estimate of the maximal overlap between the target state and pure product states and a continuous property of the geometric measure of entanglement we sh…
The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class …
Detection of quantum phase transition in spin-1 chain through multipartite high-order correlations
本研究设计了一种Bell不等式，利用多体高阶关联的广义Bell不等式形式，检测XXZ自旋1链的量子相变，在大D相与AFM相的相变区观测到明显违反，且基态呈类GHZ态，首次以此方式表征量子相变。
Recently, Fan \textit{et al.} [Mod. Phys. Lett. A 36, 2150223 (2021)], presented a generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, to identify $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states. They showed an interesting phenomenon that the maximal violation of the generalized CHSH inequality is robust under some specific noises. In this work, we map the inequality to the CHSH game, and consequently to the CHSH* game in a single-qubit system. This mapping provides an explanation for the robust violations in $N$-qubit systems. Namely, the robust violations, resulting from the degener…
We develop criteria to detect three classes of nonlocality that have been shown by Wiseman et al. [Phys. Rev. Lett. 98, 140402 (2007)] to be nonequivalent: entanglement, EPR steering, and the failure of local hidden-variable theories. We use the approach of Cavalcanti et al. [Phys. Rev. Lett. 99, 210405 (2007)] for continuous variables to develop the nonlocality criteria for arbitrary spin observables defined on a discrete Hilbert space. The criteria thus apply to multisite qudits, i.e., systems of fixed dimension d, and take the form of inequalities. We find that the spin moment inequalities …
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