Related papers: Generalized Kochen-Specker Theorem
Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
We derive inequalities for $n$ spin-1/2 systems under the assumption that the hidden-variable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one. Fine showed that this…
Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics,…
Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden…
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…
Unsharp spin observables are shown to arise from the fact that a residual uncertainty about the actual alignment of the measurement device remains. If the uncertainty is below a certain level, and if the distribution misalignments is…
The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual…
The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed…
Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from various perspectives. We emphasise the many mathematical structures intimately related to Kochen-Specker proofs, ranging through functional analysis, sheaf…
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…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
According to Pavi\v{c}i{\'c}, Kochen and Specker's 117-observable set is not a ``Kochen-Specker set''. By the same reason, in arXiv:2502.13787, Pavi\v{c}i{\'c} claims that 10 statements in our paper ``Optimal conversion of Kochen-Specker…
In recent results, it has been proven that all sampling methods produce outliers. In this paper, we extend these results to quantum information theory. Projectors of large rank must contain pure quantum states in their images that are…
We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of…
A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable…
In this talk I present a simple derivation of an old result of Kochen and Specker, which is apparently unrelated to the famous work of Bell on hidden variables, but is presumably equally important. Kochen and Specker showed in 1967 that…
The Bell-Kochen-Specker theorem (BKS) theorem rules out realistic {\it non-contextual} theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the geometrical structure of…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric…