Narrow Results

We review series of multiqubit Bell's inequalities which apply to correlation functions and present conditions that quantum states must satisfy to violate such inequalities.

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reyes' configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.

Depending on the outcome of the triphoton experiment now underway, it is possible that the new local realistic Markov Random Field (MRF) models will be the only models now available to correctly predict both that experiment and Bell's theorem experiments. The MRF models represent the experiments as graphs of discrete events over space-time. This paper extends the MRF approach to continuous time, by defining a new class of realistic model, the stochastic path model, and showing how it can be applied to ideal polaroid type polarizers in such experiments. The final section discusses possibilities for future research, ranging from uses in other experiments or novel quantum communication systems, to extensions involving stochastic paths in the space of functions over continuous space. As part of this, it derives a new Boltzmann-like density operator over Fock space, which predicts the emergent statistical equilibria of nonlinear Hamiltonian field theories, based on our previous work of extending the Glauber–Sudarshan P mapping from the case of classical systems described by a complex state variable α to the case of classical continuous fields. This extension may explain the stochastic aspects of quantum theory as the emergent outcome of nonlinear PDE in a time-symmetric universe.

For a special stochastic realistic model in certain spin-correlation experiments and without imposing the locality condition, an inequality is found. Then, it is shown that quantum theory is able (is possible) to violate this inequality. This shows that, irrespective of the locality condition, the quantum entanglement of the spin singlet-state is the reason for the violation of Bell's inequality in Bell's theorem.

In his paper,¹ Razmi derives a Bell-like inequality without imposing the locality condition. Then he shows violation of this inequality by certain quantum predictions. Here we point at a loophole in Razmi's proof, which invalidates his inequality.

Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell’s famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell’s inequality. The alternative proofs of Bell’s theorem without using Bell’s inequality are known as “nonlocality without inequality (NLWI)” proofs. We review one such proof namely the Hardy’s proof which due to its simplicity and generality has been considered the best version of Bell’s theorem.

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential element of the deterministic interpretation, we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realization of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

Recent investigations of correlations within compound physical systems are considered in the broad context, which includes “superquantum” correlations, namely, those that are stronger than predicted by standard quantum mechanics. Although the significance of these results in the search for deeper principles underlying quantum physics remains uncertain, the results do improve our understanding of quantum correlations.

We compare quantum mechanics as a theory involving probabilities to the framework of Kolmogorov's probability theory with emphasis on the connections of these theories to actual experiments. We find crucial differences in the way incompatible experiments are defined and treated in these two approaches and show that these differences are the origin for difficulties and apparent contradictions that are encountered when considering so called no-go proofs particularly that of John Bell. For example, Bell was convinced that in a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, violations of Einstein-locality must occur. Based on our comparative study, we show that rather the opposite is true and that a precise space-time treatment based on relativity uncovers contradictions in the assumptions for Bell's no-go proof and resolves the difficulties.