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Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly…

We perform numerical tests on quantum nonlocality of two-level quantum systems (qubits) observed by a uniformly moving observer. Under a suitable momentum setting, the quantum nonlocality of two-qubit nonmaximally entangled states could be…

The Greenberger-Horne-Zeilinger (GHZ) puzzle has been used to study quantum nonlocality and provide an all-or-nothing, no-go theorem for local hidden-variable models. Recent experiments using coincident-detected entangled photons prepared…

The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…

We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of…

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…

Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner's friend paradox. This is a thought experiment…

The Greenberger, Horne, Zeilinger (GHZ) theorem is critically important to consideration of the possibility of hidden variables in quantum mechanics. Since it depends on predictions of single sets of measurements on three particles, it…

Motivated by Popescu's example of hidden nonlocality, we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden variables model. We exhibit quantum states which…

One way to deal with the fact that many versions of reality simultanenously exist in the wave function is to suppose there are hidden variables that single out one version for perception. Bell showed theoretically and the Aspect experiment…

In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature…

A review of some errors made by the author and others in their search for quantum models of gravity in cosmological space-times that asymptote to de Sitter (dS) space in the future. The "static de Sitter Hamiltonian", which measures the…

In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…

We define criteria for a hidden variables theory to be Lorentz invariant and prove that it implies no signaling. As a result, we show that a Lorentz invariant and contextual theory (e.g., quantum field theory) must be genuinely stochastic,…

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)].…

The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these…

Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…

It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to…

We analyze relativistic quantum scattering in the Schr\"odinger picture. The suggestive requirement of translational invariance and conservation of the four-momentum, that the interacting Hamiltonian commute with the four-momentum $P$ of…

A time-reversal Bell test protocol is proposed. The quantum states are prepared by faraway separated partners and transferred to the third partner who carries out Bell basis measurement on them to post-select the Einstein-Podolsky-Rosen…