All multipartite Bell correlation inequalities for two dichotomic observables per site

We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit non-linear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.Comment: 11 pages, REVTe

Hidden measurements, hidden variables and the volume representation of transition probabilities

We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions $n \geq 3$. We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and their relationship with the results of Fine.Comment: 23 pages, 1 figur

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

Violations of local realism with quNits up to N=16

Predictions for systems in entangled states cannot be described in local realistic terms. However, after admixing some noise such a description is possible. We show that for two quNits (quantum systems described by N dimensional Hilbert spaces) in a maximally entangled state the minimal admixture of noise increases monotonically with N. The results are a direct extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418 (2000), where results for $N\leq 9$ were presented. The extension up to N=16 is possible when one defines for each N a specially chosen set of observables. We also present results concerning the critical detectors efficiency beyond which a valid test of local realism for entangled quNits is possible.Comment: 5 pages, 3 ps picture

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

Long-range potential fluctuations and 1/f noise in hydrogenated amorphous silicon

We present a microscopic theory of the low-frequency voltage noise (known as "1/f" noise) in micrometer-thick films of hydrogenated amorphous silicon. This theory traces the noise back to the long-range fluctuations of the Coulomb potential produced by deep defects, thereby predicting the absolute noise intensity as a function of the distribution of defect activation energies. The predictions of this theory are in very good agreement with our own experiments in terms of both the absolute intensity and the temperature dependence of the noise spectra.Comment: 8 pages, 3 figures, several new parts and one new figure are added, but no conceptual revision

Causation, Measurement Relevance and No-conspiracy in EPR

In this paper I assess the adequacy of no-conspiracy conditions employed in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these cannot be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. In the right circumstances then, violations of measurement independence need not entail any kind of conspiracy (nor backwards in time causation). To the contrary, if measurement operations in the EPR context are taken to be causally relevant in a specific way to the experiment outcomes, their explicit causal role provides the grounds for a common cause explanation of the corresponding correlations.Comment: 20 pages, 1 figur

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

Bell inequalities and distillability in N-quantum-bit systems

The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficient for full N-partite distillability. This result also allows for a security proof of multi-partite quantum key distribution (QKD) protocols.Comment: REVTEX, 12 pages, two figure