相关论文: Mermin's pentagram and Bell's theorem
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…
In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the…
It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem.…
A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's…
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…
For any state in four-dimensional system, the quantum violation of an inequality based on the Peres-Mermin proof for testing noncontextual realist models has experimentally been corroborated. In the Peres-Mermin proof, an array of nine…
Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker (KS) theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of…
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et…
For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This…
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…
The Kochen-Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics. We provide a state independent proof of the Kochen-Specker theorem using the smallest number of projectors, i.e., thirty…
The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly…
Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one,…
It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential…
We investigate small geometric configurations that furnish observable-based proofs of the Kochen-Specker theorem. Assuming that each context consists of the same number of observables and each observable is shared by two contexts, it is…
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that…
We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient…
Bell-Kochen-Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional…
A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based…
The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It…