Inequalities In Experiments Research Articles

Simulation of the Bell inequality violation based on quantum steering concept

Violation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal influence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate effects, such as deficiency of detectors and polarizers, different value of photons in each run and so on. For example, it is demonstrated, when detector efficiency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efficiency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 sqrt 2 ) otherwise maximum violation will be limited to (1.5 sqrt{2}).

Avoiding an uncertain catastrophe: climate change mitigation under risk and wealth heterogeneity

For environmental problems such as climate change, uncertainty about future conditions makes it difficult to know what the goal of mitigation efforts should be, and inequality among the affected parties makes it hard for them to know how much they each should do toward reaching the goal. We examine the effects of scientific uncertainty and wealth inequality in experiments where subjects decide how much to contribute toward reducing a common threat. We also explore how the framing of uncertainty affects collective action. Our results suggest that uncertainty lowers contributions, but contributions remain surprisingly high even in treatments with a variable loss probability, where such behavior is individually suboptimal (and where the underlying game is a prisoner’s dilemma). Further, we find that the characterization of uncertainty is crucial and that inequality need not lower contributions at all.

Collective Behavior in a Local Causal Model of Quantum Theory

The non-localities in quantum theory (QT) (the most famous example is expressed in the violation of Bell’s inequality in experiments) impede the construction of a local causal model of QT including quantum field theory (QFT). The laws of collective behavior may be considered to be types of non-local laws: laws that apply to the collection of system components as a whole. The article presents a proposal for the treatment of the non-localities that exist in QT/QFT by the concepts of collective behavior. The basic components of the collective behavior are the spatial elements of the causal model of QT/QFT proposed by the author.

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

The orthocomplemented modular lattice of subspaces ${\cal L}[H(d)]$L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice ${\cal L}[H(d)]$L[H(d)] (it is only valid within the Boolean subalgebras of ${\cal L}[H(d)]$L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator ${\mathfrak {D}}(H_1, H_2)$D(H1,H2), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors ${\mathfrak {P}}(H_1), {\mathfrak {P}}(H_2)$P(H1),P(H2), to the subspaces H1, H2. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.

Spin squeezing and entanglement for an arbitrary spin

A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-1/2 particles to entanglement conditions for spin-j particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in [A. Sorensen et al., Nature 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.