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Meyer recently queried whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision. Clifton and Kent have presented…

In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their…

Non-Gaussianity, a distinctive characteristic of bosonic quantum states, is pivotal in advancing quantum networks, fault-tolerant quantum computing, and high-precision metrology. Verifying the quantum nature of a state, particularly its…

Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands…

A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…

Two fundamental quantum resources, nonlocality and contextuality, can be connected through Bell inequalities that are violated by state-independent contextuality (SI-C) sets. These Bell inequalities allow for applications that require…

We consider the problem of representation of quantum states and observables in the framework of classical probability theory (Kolmogorov's measure-theoretic axiomatics, 1933). Our aim is to show that, in spite of the common opinion,…

Contextuality is a key feature of quantum information that challenges classical intuitions, providing the basis for constructing explicit proofs of quantum advantage. While a number of evidences of quantum advantage are based on the…

Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard,…

An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the one-particle subspace of such theories are given, both illustrating the importance of the…

Violations of Bell inequalities in classical optics have been demonstrated in terms of field mean intensities and correlations, however, the quantum meaning of violations point to statistics and probabilities. We present a violation of Bell…

The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to…

Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these…

Extensions of the Kochen-Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single…

For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…

Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science which was confirmed in the experiments proving the violation of Bell Inequalities (BI). It has been known already for a long…

We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen criterion for elements of reality and derived from the properties of some hyperentangled states allow feasible experimental verifications of the fact that quantum…

Orthofermi statistics is characterized by an exclusion principle which is more ``exclusive'' than Pauli's exclusion principle: an orbital state shall not contain more than one particle, no matter what the spin direction is. The wavefunction…

Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…

Unspeakable coherence is a key feature separating quantum and classical physics. Modelled as asymmetry with respect to a continuous transformation generated by a physically relevant observable, such as the Hamiltonian or angular moment,…