Bipartite Bell Inequality and Maximal Violation

We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum states more effectively.Comment: 6 pages,no figure

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant with respect to the value -3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in presence of a massive scalar field having a positive energy density.Comment: 31 pages, 7 figures (low resolution

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

Better detection of Multipartite Bound Entanglement with Three-Setting Bell Inequalities

It was shown in Phys. Rev. Lett., 87, 230402 (2001) that N (N >= 4) qubits described by a certain one parameter family F of bound entangled states violate Mermin-Klyshko inequality for N >= 8. In this paper we prove that the states from the family F violate Bell inequalities derived in Phys. Rev. A, 56, R1682 (1997), in which each observer measures three non-commuting sets of orthogonal projectors, for N >=7. We also derive a simple one parameter family of entanglement witnesses that detect entanglement for all the states belonging to F. It is possible that these new entanglement witnesses could be generated by some Bell inequalities.Comment: Revtex4, 1 figur

Quantum Key Distribution between N partners: optimal eavesdropping and Bell's inequalities

Quantum secret-sharing protocols involving N partners (NQSS) are key distribution protocols in which Alice encodes her key into $N-1$ qubits, in such a way that all the other partners must cooperate in order to retrieve the key. On these protocols, several eavesdropping scenarios are possible: some partners may want to reconstruct the key without the help of the other ones, and consequently collaborate with an Eve that eavesdrops on the other partners' channels. For each of these scenarios, we give the optimal individual attack that the Eve can perform. In case of such an optimal attack, the authorized partners have a higher information on the key than the unauthorized ones if and only if they can violate a Bell's inequality.Comment: 14 pages, 1 figur

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

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

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

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Multipartite Entanglement and Quantum State Exchange

We investigate multipartite entanglement in relation to the theoretical process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a novel measure called the entanglement of minimum bipartite entropy.Comment: 12 pages, 4 figure