Nonclassicality of pure two-qutrit entangled states

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.Comment: 6 pages, journal versio

Kochen-Specker Theorem for Finite Precision Spin One Measurements

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 covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.Comment: 4 page

Probability Measures and projections on Quantum Logics

The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a $G$-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied. We study such a $G$-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections. We compare properties of a $G$-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra

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

Violations of local realism by two entangled quNits are stronger than for two qubits

Tests of local realism vs quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quNits, i.e. quantum systems defined in an N-dimensional Hilbert space. Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits (N=3,4,...,9), than for two qubits and that they increase with N. The two quNit measurements can be experimentally realized using entangled photons and unbiased multiport beamsplitters.Comment: 5 pages, 2 pictures, LaTex, two columns; No changes in the result