We prove that every conceivable hidden variable model reproducing the quantum mechanical predictions of almost any entangled state must necessarily violate Bell's locality condition. The proof does not involve the consideration of any Bell inequality but it rests on simple set theoretic arguments and it works for almost any noncompletely factorizable state vector associated to any number of particles whose Hilbert spaces have arbitrary dimensionality.
Quantum nonlocality, one of the most important features of quantum mechanics, is normally connected in experiments with the violation of Bell-Clauser-Horne (Bell-CH) inequalities. We propose effective methods for the rearrangement and linear inequality to prove a large variety of Bell-CH inequalities. We also derive a set of Bell-CH inequalities by using these methods which can be violated in some quantum entangled states.
Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities
Tsinghua University（清华大学）；Universiteit Leiden（莱顿大学）；Zhejiang University（浙江大学）；Shanghai Qi Zhi Institute（上海人工智能实验室）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙大杭州全球科创中心）；Hefei National Laboratory（合肥国家实验室）
Two fundamental quantum resources, nonlocality and contextuality, can be connected through Bell inequalities that are violated by state-independent contextuality (SI-C) sets. These Bell inequalities allow for applications that require simultaneous nonlocality and contextuality. However, for existing Bell inequalities, the nonlocality produced by SI-C sets is very sensitive to noise. This precludes experimental implementation. Here we identify the Bell inequalities for which the nonlocality produced by SI-C sets is optimal, i.e., maximally robust to either noise or detection inefficiency, for t…
In this paper, combined with infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multi-partite quantum nonlocality in an infinite one-dimensional quantum spin-1/2 XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, meanwhile only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped anti-ferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order QPT (or …
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.
When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which communication and signaling is allowed. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems. In quantum mechanics, these inequalities provide device-independent witnesses for the entanglement depth. In addition, we construct a family of inequalities to detect a non-locality de…
Bell's theorem has been widely argued to show that some of the predictions of quantum mechanics which are obtained by applying the {\it Born's rule} to a class of {\it entangled states}, are {\it not} compatible with {\it any} local-causal statistical model, via the violation of Bell's inequalities. On the other hand, in the previous work, we have shown that quantum dynamics and kinematics are {\it emergent} from a statistical model that is singled out {\it uniquely} by the principle of Locality. Here we shall show that the local-causal model supports entangled states and give the statistical …
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove t…
Distinct from Bell's approach, Wigner had derived a form of local realist (LR) inequality which is quantum mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such generalised Wigner's inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present work, this limitation has been overcome by formulating a further generalisation of Wigner's approach through the derivation of a set of LR inequalities with respec…
For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell-nonlocality.
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rare…
Entanglement, EPR steering, and Bell-nonlocality criteria for multipartite higher-spin systems
我们开发的标准，以检测三类非局域性，已被证明由怀斯曼等人。[物理评论快报。98，140402（2007）]是不等价的：纠缠，EPR转向，和本地隐藏变量理论的失败。我们使用Cavalcanti等人的方法[Phys. Rev. Lett. 99，210405（2007）]的连续变量，以开发非定域性标准的任意自旋观测定义在离散希尔伯特空间。因此，该标准适用于多站点量子，即，系统的固定尺寸d，并采取不等式的形式。我们发现，当量子点数目N足够大时，优化的高关联非最大纠缠态在任意d下都可以违反检验局域隐变量的自旋矩不等式（贝尔不等式）.另一方面，纠缠的自旋不等式被违反，从而检测纠缠的状态，为任意的d和N，并与违反，增加与N.我们表明，一个时刻纠缠不等式可以检测任意广义多体格林伯格-霍恩-蔡林格状态的纠缠。因为它们涉及原子系统的自然观测量，所以相关的自旋算符关联应该在被囚禁的超冷原子气体和离子阱中容易观察到。
Homogenization proposed in [Y.-C Wu and M. Żukowski, Phys. Rev. A 85, 022119 (2012)] is a procedure to transform a tight Bell inequality with partial correlations into a full-correlation form that is also tight. In this paper, we check the homogenizations of two families of $n$-partite Bell inequalities: the Hardy inequality and the tight Bell inequality without quantum violation. For Hardy's inequalities, their homogenizations bear stronger quantum violation for the maximally entangled state; the tight Bell inequalities without quantum violation give the boundary of quantum and supra-quantum,…
Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities
North University of China（中北大学）；Beijing Institute of Technology（北京理工大学）；Taiyuan University of Technology（太原理工大学）；Southwest Jiaotong University（西南交通大学）；University of Science and Technology of China（中国科学技术大学）
We show that all $n$-qubit entangled states, with the exception of tensor products of single-qubit and bipartite maximally-entangled states, admit Hardy-type proofs of non-locality without inequalities or probabilities. More precisely, we show that for all such states, there are local, one-qubit observables such that the resulting probability tables are logically contextual in the sense of Abramsky and Brandenburger, this being the general form of the Hardy-type property. Moreover, our proof is constructive: given a state, we show how to produce the witnessing local observables. In fact, we gi…
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each observer for a maximally entangled state and two observables for a non-maximally entangled state and write down appropriate inequalities and show violation by quantum examples. Finding an example for quadratures or position and momentum is left as an open problem.
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…
The investigation of Bell nonlocality traditionally relies on joint probabilities of observing certain measurement outcomes. In this work we explore a possibilistic approach, where only patterns of possible outcomes matter, and apply it to Bell nonlocality in networks with independent sources. We present various algorithms for determining whether a given outcome pattern can be achieved via classical resources or via non-signaling resources. Next we illustrate these methods considering the triangle and square networks (with binary outputs and no inputs), identifying patterns that are incompatib…
This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of {\it the Bohr complementarity principle.} Thus, the attempts to couple experimental violations of the Bell type inequalities with "quantum nonlocality" is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single elec…
By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted …
This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party-two measurement per party-two outcomes per measurement $(2-2-2)$ Bell scenario, any argument of Bell nonlocality is a proof of trivial preparation contextuality; however, the converse may not hold. If one of the parties (say, Alice) performs the measurements of more than two dichotomic observables, then it is possible to find a set of non-trivial functional relations between Alice's observables. We argue that the existence of a suitable set of such non-trivial relations b…
The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论物理与天体物理研究所）；International Centre for Theory of Quantum Technologies, University of Gdansk（格但斯克大学量子技术理论国际中心）；Faculty of Physics, Ludwig Maximilian University（慕尼黑路德维希-马克西米利安大学物理学院）
