Higher-order tensors and tests of quantum mechanics

We illustrate a generalization of Bell's inequality which is not limited to spin-1/2 or photon systems and does not depend on model-dependent assumptions. We then construct a specific class of examples, in terms of the decaying state and the correlated observables to be measured on the decay products, for which this inequality is violated by quantum mechanics. Finally we discuss the basic and practical problems involved in the measurement of these correlations.     

Quantum logical description of two-particle systems

The quantum logical way of simulating quantum systems by automata is considered for two-particle systems. As an example, the EPR experiment with two spin-1/2 particles is considered and the violation of Bell's inequalities is demonstrated. Some methodological implications of the proposed approach are discussed.     

Simple test for hidden variables in spin-1 systems

We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.     

Bell's Theorem Without Inequalities for Arbitrarily High-Dimensional Fermionic System

A generalized proof of Bell's theorem without inequalities via the singlet state of two spin-(2n + 1)/2 fermionic particles for two observers is proposed. It is a direct and meaningful extension of that presented by A. Cabello [Phys. Rev. A67 (2003) 032107] and the proof from A. Cabello is included in our proof as a special example.     

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.     

On the possibility of a phase-space reconstruction of quantum statistics: A refutation of the Bell-Wigner locality argument

J. S. Bell's argument that only nonlocal hidden variable theories can reproduce the quantum statistical correlations of the singlet spin state in the case of two separated spin-1/2 particles is examined in terms of Wigner's formulation. It is shown that a similar argument applies to a single spin-1/2 particle, and that the exclusion of hidden variables depends on an obviously untenable assumption concerning conditional probabilities. The problem of completeness is discussed briefly, and the grounds for rejecting a phase-space reconstruction of the quantum statistics are clarified.Research supported by the National Science Foundation.     

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.     

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.     

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.     

Phase Diagrams of a Transverse Ising Model with Interfaces

A transverse Ising model for a magnetic superlattice of spin-1/2 Ising layered media intercalated by periodic interfaces described by the spin-1/2 Ising model is considered. Phase diagrams and different profiles of magnetization determined by the parameters of the model are discussed within a variational procedure based on Bogoliubov's inequality for the free energy. Our results agree to those of the other's work at the limit of Ω = 0.     

Local reality: Can it exist in the EPR-Bohmgedanken experiment?

Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR-Bohm gedanken experiment.     

Entanglement in 2DEG systems: towards a detection loophole-free test of Bell's inequality

We make use of the intrinsic noiseless and lossless aspect of an electron source in a 2DEG system to implement a new test of Bell's inequality. The generated entanglement can be tested by two-particle interferometry. Preparation and detection schemes of two complete sets of Bell states are given. A novel type of Bell's inequality is then derived in terms of noise correlation measurements. The characteristics of the electron source are essential to exhibit a violation. This electron system could close the detection efficiency loophole.     

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.     

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.     

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.     

Bell’s Theorem Without Inequalities and Only Two Distant Observers

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.     

Phase transitions and multicritical points in the mixed spin-3/2 and spin-2 Ising model with different single-ion anisotropies

The phase diagram of mixed spin-3/2 and spin-2 Ising ferromagnetic model with different single-ion anisotropies is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular, by changing values of the single-ion anisotropies, several different types of phase diagrams of first-order transition between two ordered phases, are studied in detail. A variety of multicritical points such as tricritical points, isolated critical points, and triple points are obtained.     

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.     

A remark on Bell's inequality and decomposable normal states

Bell's correlation inequality is considered in the algebraic framework as discussed by Baez. It is shown that all normal states of the tensor product of two W ^*-algebras satisfy Bell's inequality, if and only if every normal state lies in the closure of the convex hull of the normal product states, if and only if one of the algebras is commutative.     

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.