Unified scheme for correlations using linear relative entropy

A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which we determine the total, classical and quantum correlations. We also give the explicit expressions of its closest product state, closest classical state and the corresponding closest product state. A closed additive relation, involving the various correlations quantified by linear relative entropy, is derived.Comment: 20 page

Topological String on Toric CY3s in Large Complex Structure Limit

We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that purpose, we first consider the $T^{2}\times R$ special Lagrangian fibration of generic CY3-folds and we give the realization of the class of large $\mu$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials $)$. Then, we focus on a one complex parameter supersymmetric $U(1)$ gauged model involving six chiral superfields ${\Phi_{i}}$ with $\mathcal{W}=\mu (\prod\nolimits_{i=0}^{5}\Phi_{i})$ and we use it to compute the function $\mathcal{Z}_{top}$ for the case of the local elliptic curve in the limit $\mu \to \infty$.Comment: Latex, 38 pages, 12 figures. To appear in Nucl Phys

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.Comment: 26 page

Type II seesaw supersymmetric neutrino model for θ13≠0\theta_{13}\neq0

Using the type II seesaw approach and properties of discrete flavor symmetry group representations, we build a supersymmetric $A_{4}\times A_{3}$\ neutrino model with $\theta_{13}\neq0$. After describing the basis of this model--which is beyond the minimal supersymmetric Standard Model--with a superfield spectrum containing flavons in $A_{4}\times A_{3}$\ representations, we first generate the tribimaximal neutrino mixing which is known to be in agreement with the mixing angles $\theta_{12}$ and $\theta_{23}$. Then, we give the scalar potential of the theory where the $A_{3}$ discrete subsymmetry is used to avoid the so-called sequestering problem. We \textrm{next} study the deviation from the tribimaximal mixing matrix which is produced by perturbing the neutrino mass matrix with a nontrivial $A_{4}$ singlet. Normal and inverted mass hierarchies are discussed numerically. We also study the breaking of $A_{4}$\ down to $Z_{3}$\ in the charged lepton sector, and use the branching ratio of the decay $\tau \rightarrow \mu \mu e$--which is allowed by the residual symmetry $Z_{3}$--to get estimations on the mass of one of the flavons and the cutoff scale $\Lambda$ of the model.Comment: 45 pages, 4 figures, LaTe