Related papers: Strong Kochen-Specker theorem and incomputability …
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…
One of the recent no-go theorems on \Psi-epistemic interpretations of quantum proves that there are no 'maximally epistemic' interpretations of quantum theory. The proof utilises similar arrangements to Clifton's quantum contextuality proof…
We propose an experimental approach to {\it macro}scopically test the Kochen-Specker theorem (KST) with superconducting qubits. This theorem, which has been experimentally tested with single photons or neutrons, concerns the conflict…
Within the framework of quantum contextuality, we discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. We emphasize that whereas Kochen-Specker's is essentially a no-go…
While non-contextual hidden-variable theories are proved to be impossible, contextual ones are possible. In a contextual hidden-variable theory, an observable is called a beable if the hidden-variable assigns its value in a given…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…
Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists…
It is shown that, given a reasonable continuity assumption regarding possessed values, it is possible to construct a Kochen-Specker obstruction for any coordinate and its conjugate momentum, demonstrating that at most one of these two…
Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems.…
One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as…
Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some…
For the first time we construct an infinite family of Kochen-Specker sets in a space of fixed dimension, namely in R^4. While most of the previous constructions of Kochen-Specker sets have been based on computer search, our construction is…
The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We…
It is shown that quantum-type coherence, leading to indeterminism and interference of probabilities, may in principle exist in the absence of the Planck constant and a Hamiltonian. Such coherence is a combined effect of a symmetry (not…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful…
We construct a non-contextual hidden variable model consistent with all the kinematic predictions of quantum mechanics (QM). The famous Bell-KS theorem shows that non-contextual models which satisfy a further reasonable restriction are…