Numerical Simulation of Bell Inequality's Violation Using Optical Transverse Modes in Multimode Waveguides

We numerically demonstrate that ＇mode-entangled states＇ based on the transverse modes of classical optical fields in multimode waveguides violate Bell＇s inequality. Numerically simulating the correlation measurement scheme of Bell＇s inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell＇s inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.     

Stronger-Than-Quantum Correlations

After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.     

Quantum communication complexity protocol with two entangled qutrits

We formulate a two-party communication complexity problem and present its quantum solution that exploits the entanglement between two qutrits. We prove that for a broad class of protocols the entangled state can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bell's inequality for two qutrits.     

Criticizing Bell: Local realism and quantum physics reconciled

A typical sample of Bell's inequality is proved to require, besides the standard assumptions on realism and locality, the adoption of a metatheoretical classical principle for interpreting quantum laws. A new principle is proposed which is consistent with the operational philosophy of quantum physics; it is then shown that, whenever the latter principle is adopted in place of the former, realism (here intended in a purely semantical sense) and locality do not imply Bell's inequality in the form considered here, but a new inequality which is not violated in quantum physics. Thus an interpretation of quantum physics that is (semantically) realistic and local is suggested, which eliminates a number of seeming paradoxes.     

Violations of Bell's Inequality in Synchronized Hyperchaos

Motivated by a parallel between quantum cryptography and chaos synchronization cryptography, we construct a Bell's inequality for a pair of synchronously coupled variable-order Generalized Rossler Systems, with arbitrarily binarized final states. In the infinite-order limit, although dynamical parameters cannot be extracted from the coupling signal in finite time, the inequality is violated, as with entangled quantum states. The violations are weaker than in quantum theory, vanishing as the differences between corresponding parameters of the coupled systems become small. The fact that Bell's inequality can be violated for a pair of classical systems that are not discernibly connected supports the possibility of a realist interpretation of quantum mechanics.     

The geometry of violation of Bell''''s inequality

The purpose of this paper is to deduce an analytical expression for the violation of Bell's inequality by quantum theory and plane trigonometry, and expound the violation and maximal violation of the first, second type Bell's inequality in detail. Further, we find out the sufficient conditions for the region in which Bell's inequalities are violated.     

Stronger two-observer all-versus-nothing violation of local realism

We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell inequality which resembles Mermin's inequality for three observers but requires only two observers.     

Testing locality at colliders via Bell''s inequality?

We consider a measurement of correlated spins at LEP and show that it does not constitute a general test of local-realistic theories via Bell's inequality. The central point of the argument is that such tests, where the spins of two particles are inferred from a scattering distribution, can be described by a local hidden variable theory. We conclude that with present experimental techniques it is not possible to test locality via Bell's inequality at a collider experiment. Finally we suggest an improved fixed-target it is not possible to test locality via Bell's inequality at a collider experiment. Finally we suggest an improved fixed-target experiment as a viable test of Bell's inequality.     

Bell's Inequality for a System Composed of Particles with Different Spins

For two particles with different spins, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and spin-1/2; spin-1/2 and spin-3/2. We show that for these states Bell's inequality is violated.     

Electron entanglement detected by quantum spin Hall systems

We propose a promising electron entanglement detector consisting of two quantum spin Hall systems weakly coupled to a superconductor. The detection of electron spins along various polarization directions, which is a prerequisite for testing Bell's inequality on solid state spins, can be achieved in an all-electrical-controlled manner utilizing the helical edge states. It is found that the violation of Bell's inequality exists in a large range of the tunneling parameters, which can be realized in mercury telluride quantum wells.     

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.     

Bell's inequality forC *-algebras

Bell's inequality dealing with local hidden variables is given two formulations in terms ofC ^*-algebras. In particular, Bell's inequality holds for all states onAB wheneverA andB are unitalC ^*-algebras at least one of which is Abelian, i.e., at least one corresponds to a classical physical system.     

Testing quantum nonlocality for three coupled quantum dots within optical microcavity QED

Bell's inequality for three coupled quantum dots (QDs) within a cavity QED, including Förster and exciton-phonon interactions, is investigated theoretically. For an initially entangled state, Bell's inequality is valid for certain times and violated for some other times. It is shown that the system moves from a product state to an entangled state and back again during its time evolution.     

Nonlocality and Multipartite Entanglement in Asymptotically Flat Space-Times

We study the Bell's inequality and multipartite entanglement generation for initially maximally entangled states of free Dirac field in a non inertial frame and asymptotically flat Robertson–Walker space-time.For two qubit case,we show that the Bell's inequality always is violated as measured by the accelerated observers which are in the causally connected regions.On the other hand,for those observers in the causally disconnected regions inequality is not violated for any values of acceleration.The generated three qubit state from two qubit state due to acceleration of one parties has a zero 3-tangle.For a three qubit state,the inequality violated for measurements done by both causally connected and disconnected observers.Initially GHZ state with non zero 3-tangle,in accelerated frame,transformed to a four qubit state with vanishing 4-tangle value.On the other hand,for a W-state with zero 3-tangle,in non inertial frame,transformed to a four qubit state with a non-zero 4-tangle acceleration dependent.In an expanding space-time with asymptotically flat regions,for an initially maximally entangled state,the maximum value of violation of Bell's inequality in the far past decreased in the far future due to cosmological particle creation.For some initially maximally entangled states,the generated four qubit state due to expansion of space-time,has non vanishing 4-tangle.     

Classical Versions of q-Gaussian Processes:¶Conditional Moments and Bell's Inequality

We show that classical processes corresponding to operators which satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell's inequality for their covariances can be extended from q=−1 to the entire range −1≤q < 1. Received: 18 September 2000 / Accepted: 17 November 2000     

从贝尔不等式到量子信息"热"

介绍了贝尔不等式的建立及20世纪70年代以来对它的实验验证．对贝尔不等式与量子力学基本解释的关系的深入研究,加速了“纠缠态”及其品性的发现,推动了量子信息“热”的兴起。     

Experimental violation of Bell's inequality in spatial-parity space

We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.     

Nonlocal information as condition for violations of Bell inequality and information causality

On the basis of local realism theory, nonlocal information is necessary for violation of Bell's inequality. From a theoretical point of view, nonlocal information is essentially the mutual information on distant outcome and measurement setting. In this work we prove that if the measurement is free and unbiased, the mutual information about the distant outcome and setting is both necessary for the violation of Bell's inequality in the case with unbiased marginal probabilities. In the case with biased marginal probabilities, we point out that the mutual information about distant outcome cease to be necessary for violation of Bell's inequality, while the mutual information about distant measurement settings is still required. We also prove that the mutual information about distant measurement settings must be contained in the transmitted messages due to the freedom of measurement choices. Finally we point out that the mutual information about both distant outcome and measurement settings are necessary for a violation of information causality.     

Proposed experiment to test the bounds of quantum correlations

The combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 x square root of 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell's inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.     

Quantum α-entropy inequalities: independent condition for local realism?

Quantum α-entropy inequalities equivalent to Bell's inequality for pure states are considered in the context of the local hidden variable (LHV) model and compared with Bell's inequalities. For α = 1,2 they are shown to be satisfied by convex combinations of product states and Werner's mixtures admitting the model. The 2-entropy inequality is proven to be stronger than Bell's inequality in the case. In the latter, the α-entropy inequalities taken as a joint condition exclude teleportation admitted in spite of the existence of the LHV model for the Werner-Popescu states.