Nonlocality of two- and three-mode continuous variable systems
A. Ferraro, M. G. A. Paris
备注：
17 pages, 7 figures. A paragraph concerning the choice of the displacement parameters has been added (Sec. 3.1). References and comparison with other proposals added (Sec. 4)
We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also considered as a conditional source of two-mode non Gaussian states, whose nonlocal properties are analyzed. We found that the non Gaussian character of the conditional states allows violation of Bell's inequalities (by parity and pseudospin tests) stronger than with a conventional twin-beam state. However, the non Gaussian character is not sufficient to reveal nonlocality thorough a dichotomized quadrature measurement strategy.
An experiment has recently been performed to demonstrate quantum nonlocality by establishing contextuality in one of a pair of photons encoding four qubits; however, low detection efficiencies and use of the fair-sampling hypothesis leave these results open to possible criticism due to the detection loophole. In this Letter, a physically motivated local hidden-variable model is considered as a possible mechanism for explaining the experimentally observed results. The model, though not intrinsically contextual, acquires this quality upon post-selection of coincident detections.
Uncertainty principle is one of the central concepts in quantum theory. Different forms of this particular principle have been discoursed in various foundational and information theoretic topics. In the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by fine-grained uncertainty relation. On the other hand, in continuous variable paradigm Robertson-Schrodinger (RS) uncertainty relation has been used to detect multi-mode entanglement. Here we show that RS uncertainty relation plays an important role to discriminate between quantum and post-quantu…
Greenberger-Horne-Zeilinger nonlocality for continuous variable systems
作为我们以前工作的发展，本文研究了连续变量情形下的Greenberger-Horne-Zeilinger（GHZ）非定域性。讨论的基础上引入一个赝自旋算子，它具有相同的代数的泡利算子，为每一个$N$模式的光场。然后，对具有连续自由度的$N$模态，给出了Bell-CHSH（Clauser，Horne，Shimony and Holt）不等式.根据Mermin的论证，我们证明了在无限维Hilbert空间中，对于$N$模宇称纠缠的GHZ态，量子力学与局域实在论之间的矛盾随着$N$呈指数增长，类似于通常的$N$ -自旋情形.
The study of nonlocality in scenarios that depart from the bipartite Einstein-Podolsky-Rosen setup is allowing to uncover many fundamental features of quantum mechanics. Recently, an approach to building network-local models based on machine learning lead to the conjecture that the family of quantum triangle distributions of [arXiv:1905.04902] did not admit triangle-local models in a larger range than the original proof. We prove part of this conjecture in the affirmative. Our approach consists in reducing the family of original, four-outcome distributions to families of binary-outcome ones, a…
Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in post-quantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devic…
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…
Robust Bell Nonlocality from Gottesman-Kitaev-Preskill States
Center for Macroscopic Quantum States bigQ, Department of Physics, Technical University of Denmark（丹麦技术大学宏观量子态中心bigQ）；Physics Department, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学物理系）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；School of Science and Technology, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学理学院）
We consider a multiphoton Bell-type inequality to study nonlocality in four-mode continuous variable systems, which goes beyond two-photon states and can be applied to mixed as well as states with fluctuating photon number. We apply the inequality to a wide variety of states such as pure and mixed Gaussian states (including squeezed thermal states) and non-Gaussian states. We consider beam splitters as a model for leakage and show that the inequality is able to detect nonclassicality of noisy Gaussian states as well. Finally, we investigate nonlocality in pair-coherent states and entangled coh…
In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein-Podolsky-Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via a nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can …
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme tha…
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。
Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach-Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geom…
Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state: \begin{align} \nonumber ρ_α= α\,|Φ^+ \rangle\langle Φ^+|+(1-α)\frac{\mathbb{1}}{4}. \end{align} We present two main results, consi…
Device independent protocols based on Bell nonlocality, such as quantum key distribution and randomness generation, must ensure no adversary can have prior knowledge of the measurement outcomes. This requires a measurement independence assumption: that the choice of measurement is uncorrelated with any other underlying variables that influence the measurement outcomes. Conversely, relaxing measurement independence allows for a fully `causal' simulation of Bell nonlocality. We construct the most efficient such simulation, as measured by the mutual information between the underlying variables an…
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.
We propose an optimal numerical test for genuine multipartite nonlocality based on linear programming. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal model. While our knowledge concerning these models is well established for Bell scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine $n…
Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the nonlocality present in a single particle from an entangled pair using the method of weak measurements [Phys. Rev. Lett. {\bf 114}, 250401 (2015)]. Here we report an observation of double CHSH…
