Bell's theorem without inequalities and without unspeakable information

A proof of Bell's theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.Comment: REVTeX4, 4 pages, 1 figure; for Asher Peres' Festschrift, to be published in Found. Phy

Kochen-Specker Sets and Generalized Orthoarguesian Equations

Every set (finite or infinite) of quantum vectors (states) satisfies generalized orthoarguesian equations ($n$OA). We consider two 3-dim Kochen-Specker (KS) sets of vectors and show how each of them should be represented by means of a Hasse diagram---a lattice, an algebra of subspaces of a Hilbert space--that contains rays and planes determined by the vectors so as to satisfy $n$OA. That also shows why they cannot be represented by a special kind of Hasse diagram called a Greechie diagram, as has been erroneously done in the literature. One of the KS sets (Peres') is an example of a lattice in which 6OA pass and 7OA fails, and that closes an open question of whether the 7oa class of lattices properly contains the 6oa class. This result is important because it provides additional evidence that our previously given proof of noa =< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure

On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits

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 small $v-l$ BKS-proofs involving $v$ real rays and $l$ $2n$-dimensional bases of $n$-qubits ($1< n < 5$). Specifically, we look at the parity proof 18-9 with two qubits (A. Cabello, 1996), the parity proof 36-11 with three qubits (M. Kernaghan & A. Peres, 1995 \cite{Kernaghan1965}) and a newly discovered non-parity proof 80-21 with four qubits (that improves work of P. K Aravind's group in 2008). The rays in question arise as real eigenstates shared by some maximal commuting sets (bases) of operators in the $n$-qubit Pauli group. One finds characteristic signatures of the distances between the bases, which carry various symmetries in their graphs.Comment: version to appear in European Physical Journal Plu

Entangled qutrits violate local realism stronger than qubits - an analytical proof

In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled $N$-dimensional ($3 \leq N$) quantum objects is stronger than for two maximally entangled qubits and grows with $N$. In this paper we present the analytical proof of this fact for N=3.Comment: 5 page

Observables have no value: a no-go theorem for position and momentum observables

A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments adde

Bohm's interpretation and maximally entangled states

Several no-go theorems showed the incompatibility between the locality assumption and quantum correlations obtained from maximally entangled spin states. We analyze these no-go theorems in the framework of Bohm's interpretation. The mechanism by which non-local correlations appear during the results of measurements performed on distant parts of entangled systems is explicitly put into evidence in terms of Bohmian trajectories. It is shown that a GHZ like contradiction of the type+1=-1 occurs for well-chosen initial positions of the Bohmian trajectories and that it is this essential non-classical feature that makes it possible to violate the locality condition.Comment: 18 page

Bell's inequalities for states with positive partial transpose

We study violations of n particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system into p subsystems are positive, the best upper bound on the violation is 2^((n-p)/2). In particular, if the partial transposes with respect to all subsystems are positive, the inequalities are satisfied. This is supporting evidence for a recent conjecture by Peres that positivity of partial transposes could be equivalent to existence of local classical models.Comment: 4 pages, REVTe

State-independent quantum violation of noncontextuality in four dimensional space using five observables and two settings

Recently, a striking experimental demonstration [G. Kirchmair \emph{et al.}, Nature, \textbf{460}, 494(2009)] of the state-independent quantum mechanical violation of non-contextual realist models has been reported for any two-qubit state using suitable choices of \emph{nine} product observables and \emph{six} different measurement setups. In this report, a considerable simplification of such a demonstration is achieved by formulating a scheme that requires only \emph{five} product observables and \emph{two} different measurement setups. It is also pointed out that the relevant empirical data already available in the experiment by Kirchmair \emph{et al.} corroborate the violation of the NCR models in accordance with our proof

Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been correcte

Functional Bell inequalities can serve as a stronger entanglement witness

We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This "functional" Bell inequality gives a better range of violation for generalized GHZ states. Also a family of N-qubit bound entangled states violate this inequality for N>5.Comment: 4 pages, REVTeX