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Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called…
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the…
Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be…
Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should…
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 argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second,…
We report two fundamental experiments on three-level quantum systems (qutrits). The first one tests the simplest task for which quantum mechanics provides an advantage with respect to classical physics. The quantum advantage is certified by…
The precession protocol involves measuring $P_3$, the probability that a uniformly precessing observable (like the position of a harmonic oscillator or a coordinate undergoing spatial rotation) is positive at one of three equally spaced…
Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to…
Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…
Bell's inequality sets a strict threshold for how strongly correlated the outcomes of measurements on two or more particles can be, if the outcomes of each measurement are independent of actions undertaken at arbitrarily distant locations.…
The relation between quantum theory and special relativity is peculiar. On the one hand it is close and essential. Steven Weinberg [1], for example, takes the position that the standard model is an inevitable consequence of the marriage of…
Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical…