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Cyclic quantum teleportation schemes requires at least the existence of three collaborators acting all as senders and receivers of quantum information, each one of them has an information to be transmitted to the next neighbour in a circular manner. Here, new cyclic quantum teleportation scheme is proposed for perfectly transmitting cyclically three arbitrary unknown two-qubit states ($\alpha$, $\beta$ and $\gamma$) among the three collaborators. In this scheme, Alice can send to Bob the quantum information contained in her two-qubit state $\alpha$ and receive from Charlie the quantum information contained in the two-qubit state in his possession $\gamma$ and similarly, Bob can transmit to Charlie the quantum information contained in his two-qubit state $\beta$ through a quantum channel of twelve-qubit state consisting of a six-qubit cluster state and a six-qubit entangled state by sequentially and cyclically performing Bell state measurements. Subsequently, each one of the three participants can afterwards retrieve his own desired two-qubit state using classical channel and by performing appropriate unitary Pauli operators and we have shown that our proposed scheme performs efficiently.

The Asymptotic WGC has been proposed as a special case of the tower WGC that probes infinite distances in the moduli space corresponding to weakly coupled gauge regimes. The conjecture has been studied in M-theory on Calabi-Yau threefold (CY3) with finite volume inducing a 5D effective QFT. In this paper, we extend the scope of the previous study to encompass lower dimensions, particularly we generalise the obtained 5D asymptotic WGC to the effective field theory $EFT_{3D}$ coupled to 3D gravity that descends from M-theory compactified on Calabi-Yau fourfold with an emphasis on K3 x K3. We find that the CY4 has three fibration structures labelled as line Type-$T^2$, surface Type-$S$ and bulk Type-$V$. The emergent $EFT_{3D}$ is shown to have 2+2 towers of states occupied by light and heavy BPS as well as non BPS particles. To ensure the viability of the 3D Asymptotic WGC, we give explicit calculations to thoroughly test the swampland constraint for both the weakly and strongly gauge coupled regimes. Additional aspects, including the gauge symmetry breaking and duality symmetry are also investigated.

Secrecy and security are crucial in communication. So, quantum secret sharing protocol has recently been proposed to distribute a secret message to a set of parties, where the decoding procedure is forbidden individually, and a cooperative operation is needed. For this, quantum steering as an intriguing kind of nonlocality, is proven to be a useful resource for efficient implementations of the QSS protocol. Here, we study the distribution of Gaussian steering over an asymmetric three-mode optomechanical state. We show that a single-mode cannot be jointly steered by the two others, and further verify the monogamy inequalities of Gaussian steering. The state at hand displays genuine tripartite steering. Also, we observe one-way steering in the configuration (1vs1) mode as well as (1vs2) mode, hence, we reveal that the asymmetry introduced into the state we consider, is a necessary condition but not sufficient for reaching one way steering. As well, we detect one-way steering between two modes never directly interact. Strikingly, our model exhibits an extreme level of steering, where two single-mode cannot steer individually the third mode, while, they can collectively, which is decisive for practical execution of the QSS protocol.

In this study, we investigate the electronic, optical, thermoelectric, and thermodynamic properties of Ca(InP)2 through comprehensive theoretical calculations Ca(InP)2 is a compound with promising applications in materials science and electronics. Using the density functional theory (DFT) with Generalized Gradient Approximation (GGA) and modified Becke_Johnson approximation (mBJ), we determine the band structure, density of states, and optical properties of Ca(InP)2. The obtained results reveal that the Ca(InP)2 compound exhibits a direct band gap of 0 eV and 0,645 eV for PBE-GGA and GGA+mBJ, respectively. This direct band gap is found at the Gamma point of the Brillouin zone, making it well-suited for optoelectronic applications. Furthermore, we analyze the thermoelectric properties such as the Seebeck coefficient, the lattice thermal conductivity, and optical properties like dielectric function, absorption coefficient, conductivity, and extinction coefficient. Thermodynamic properties, including heat capacity and Debye temperature, are also calculated, providing a deeper understanding of the compound's thermal behavior. The findings of this study highlight the fundamental characteristics of Ca(InP)2 and offer valuable information for its potential use in electronic and optoelectronic devices. A comprehensive understanding of the electronic, optical, and thermodynamic properties of the Ca(InP)2 compound can serve as a guide for future experimental research and aid in the design of novel materials for a wide range of technological applications.

Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its embedding in string theory. Because of the $\mathbb{Z}_{2}$-grading of $ sl(m|n)$, we show that the $\left( m+n\right) !/m!n!$ varieties of superspin chains with underlying super geometries have different cycle homologies. We investigate the algebraic and homological features of these integrable quantum chains and give a link between graded 2-cycles and genus-g Rieman surfaces $\Sigma _{g}$. Moreover, using homology language, we yield the brane realisation of the $sl(m|n)$ chain in type IIA string and its uplift to M-theory. Other \textrm{aspects} like graded complex surfaces with $sl(m|n)$ singularity as well as super magnons are also described., Comment: LaTeX, 60 pages, 18 figures

We give Swampland constraints for the three dimensional Landscape of Anti-de Sitter gravity in the Chern-Simons formulation with connection valued in various split real forms of Lie algebras. We derive explicitly the limit on the number of massless modes by computing the upper bound on the rank of possible gauge groups and thus validating this Swampland conjecture in 3D. We discuss the implications of this constraint on the spectrum of higher spin gravity theories and we compare it with the gravitational exclusion principle required from BTZ black hole consideration to excerpt a constraint on the Chern-Simons level k., Comment: LaTeX, 43 pages, 8 Figures

We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax matrices verifying the RLL integrability equation. We propose gauge quiver diagrams Q$_{G}^{\mu }$ encoding the topological data carried by the Lax operators and give several examples where Darboux coordinates are interpreted in terms of topological bi-fundamental matter. We exploit this graphical description $\left( i\right) $ to give new results regarding solutions in representations beyond the fundamentals of $sl_{N}$, $% so_{2N}$ and $e_{6,7}$, and $\left( ii\right) $ to classify the Lax operators for simply laced symmetries in a unified E$_{7}$ CS theory. For quick access, a summary list of the leading topological quivers Q$% _{ADE}^{\mu }$ is given in the conclusion section [Figures 29.(a-e), 30.(a-d) and 31.(a-d)]., Comment: LaTeX, 74 pages, 32 figures

We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the $SL\left( m|n\right) $ super-group family. From this theory, we derive the oscillator realisation of the Lax operator for superspin chains with $SL(m|n)$ symmetry. To this end, we investigate the holomorphic property of the bosonic Lax operator $\mathcal{L}$ and build a differential equation $% \mathfrak{D}\mathcal{L}=0$ solved by the Costello-Gaioto-Yagi realisation of $\mathcal{L}$ in the framework of\ the CS theory. We generalize this construction to the case of gauge super-groups, and develop a Dynkin super-diagram algorithm to\ deal with the decomposition of the Lie superalgebras. We obtain the generalisation of the Lax operator describing the interaction between the electric Wilson super-lines and the magnetic 't Hooft super-defects. This coupling is given in terms of a mixture of bosonic and fermionic oscillator degrees of freedom in the phase space of magnetically charged 't Hooft super-lines. The purely fermionic realisation of the superspin chain Lax operator is also investigated and it is found to coincide exactly with the $\mathbb{Z}_{2}$- gradation of Lie superalgebras.\ \newline Keywords: 4D Chern-Simons theory, Super-gauge symmetry, Lie superalgebras and Dynkin super-diagrams, Superspin chains and integrability, Super- Lax operator., Comment: LaTeX, 55 pages, 8 figures

Quantum teleportation of an unknown state basing on the interaction between discrete-valued states (DV) and continuous-valued states (CV) presented a particular challenge in quantum technologies. Here we consider the problem of controlled quantum teleportation of an amplitude-matched CV qubit, encoded by a coherent state of a varied phase as a superposition of the vacuum- and single-photon optical states among two distant partners Alice and Bob, with the consent of controller, Charlie. To achieve this task, we use an hybrid tripartite entangled state (interaction between the discrete and continuous variables states) as the quantum resource where the coherent part belongs to Alice, while the single-photon belongs to Bob and Charlie and the CV qubit is at the disposal of Alice. The discrete-continuous interaction is realized on highly transmissive beam-splitter. We have shown that the perfectly of teleportation fidelity depends on the phase difference between the phase of the state to teleport and the phase of the sender's mode, we found that for a difference which approaches 0 or $\pi$, near perfect controlled quantum teleportation can be obtained in terms of the fidelity and independently of the amplitude $\alpha$ and the squeezing parameter $\zeta$. Experimentally, this proposed scheme has been implemented using linear optical components such as beam splitter, phase shifters and photon counters., Comment: Published version in Physica Scripta

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in the multi-component quantum system [S. Kim et al., Phys. Rev. A. 97, 032326 (2018)]. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg $XY$ model. Two distinct situations are considered. The first one concerns the anisotropic $XY$ model and the second situation concerns the isotropic $XY$ model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU., Comment: 16 pages, 8 figures

The quantum Fisher information matrix provides us with a tool to determine the precision, in any multiparametric estimation protocol, through quantum Cram\'er-Rao bound. In this work, we study simultaneous and individual estimation strategies using the density matrix vectorization method. Two special Heisenberg $XY$ models are considered. The first one concerns the anisotropic $XY$ model in which the temperature $T$ and the anisotropic parameter $\gamma$ are estimated. The second situation concerns the isotropic $XY$ model submitted to an external magnetic field $B$ in which the temperature and the magnetic field are estimated. Our results show that the simultaneous strategy of multiple parameters is always advantageous and can provide a better precision than the individual strategy in the multiparameter estimation procedures., Comment: 21 pages, 10 figures

We explore the spontaneous generation and decay of quantum correlations between two identical atoms coupled to a common Markovian environment in the presence of electromagnetic field modes. For this purpose, we analyze the dynamics of quantum correlations by employing the concurrence, the trace quantum discord and the local quantum uncertainty, for collective Dicke states. It is shown that the collective damping and dipole-dipole interaction plays a key role in enhancing non-classical correlations during the process of intrinsic decoherence. The quantum correlations can be maintained over a long time but for small distance between the two atoms., Comment: 10 Pages, 12 Figures

We propose a next-to-minimal supersymmetric Standard Model (NMSSM) extended by an $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ flavor symmetry and three right-handed neutrinos providing a detailed study of the neutrino sector and a solution to the domain wall problem. In this proposal, neutrino masses are generated through Type I seesaw mechanism while the mixing angles are described by the trimaximal mixing realized using the NMSSM singlet S and only two flavon fields. The phenomenology of neutrino parameters is studied for normal and inverted mass hierarchies. In particular, we numerically evaluated the observables related to neutrino masses and mixing, namely, $\sum m_{i}$, $m_{ee}$, $m_{\nu_{e}}$, and $\delta_{CP}$ where we find that the ranges of $m_{ee}$ and $m_{\nu_{e}}$ are accessible by current and future experiments while the obtained ranges of $\sum m_{i}$ and $\delta_{CP}$ lie within the current experimental data. Another attractive feature we discussed in this paper is the circumvention of the domain wall problem induced by the spontaneous breaking of the $\mathbb{A}_{4}\times \boldsymbol{Z}_{3}$ discrete symmetry. We first showed that the domain walls in the charged lepton sector occur at high energy scale leading to unproblematic domain walls, while in the neutrino sector they are inevitable. Then, to solve this problem, we reconsidered the well-known approach that relies on the explicit breaking of the discrete symmetry through the insertion of Planck-suppressed operators induced by supergravity. \keywords{Neutrino physics, Discrete flavor symmetry,Trimaximal mixing, Domain walls}, Comment: 43 pages, 13 figures. Published version

The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas, the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach simultaneous three bipartite entanglements via the quantum correlations transfer from the squeezed light to the system. While, even without squeezed light, the quantumness of correlations can be captured simultaneously between the three modes for a very wide range of parameters. Specifically, we find that the two optical modes exhibit more quantum correlations in comparison with the entangled mechanical-optical modes. Finally, unlike the two hybrid subsystems, the purely optical one seems more resilient against the environmental destructive effects.

Motivated by recent results from neutrino experiments, we study the neutrino masses and mixing in the framework of a SUSY $SU(5)\times \mathbb{A}_{4} $ model. The hybrid of Type I and Type II seesaw mechanisms leads to the nonzero value of the reactor angle $\theta_{13}\neq 0$ and to the recently disfavored maximal atmospheric angle $\theta_{23} \neq45^{\circ}$ by the NOvA experiment. The phenomenological consequences of the model are studied for both normal and inverted mass hierarchies. The obtained ranges for the effective Majorana neutrino mass $m_{\beta \beta}$, the electron neutrino mass $m_{\nu_{e}}$, and the $CP$ violating phase $\delta_{CP}$ lie within the current experimental allowed ranges where we find that the normal mass hierarchy is favored over the inverted one., Comment: 27 pages, 10 figures, REVTeX

Using a new manner to rescale fields in $\mathcal{N}=2$ gauged supergravity with n$_{V}$ vector multiplets and n$_{H}$ hypermultiplets, we develop the explicit derivation of the rigid limit of quaternionic isometry Ward identities agreeing with known results. We show that the rigid limit can be achieved, amongst others, by performing two successive transformations on the covariantly holomorphic sections $V^{M}\left( z,\bar{z}\right) $ of the special Kahler manifold: a particular symplectic change followed by a particular Kahler transformation. We also give a geometric interpretation of the $\eta_{i}$ parameters used in arXiv:1508.01474 to deal with the expansion of the holomorphic prepotential $\mathcal{F}\left( z\right) $ of the $\mathcal{N}=2$ theory. We give as well a D- brane realisation of gauged quaternionic isometries and an interpretation of the embedding tensor $\vartheta_{M}^{u}$ in terms of type IIA/IIB mirror symmetry. Moreover, we construct explicit metrics for a new family of $4r$- dimensional quaternionic manifolds $\boldsymbol{M}_{QK}^{\left( n_{H}\right) }$ classified by ADE Lie algebras generalising the $SO\left( 1,4\right) /SO\left( 4\right) $ geometry which corresponds to $A_{1}\sim su\left( 2\right) $. The conditions of the partial breaking of $\mathcal{N}=2$ supersymmetry in the rigid limit are also derived for both the observable and the hidden sectors. Other features are also studied., Comment: LaTeX, 89 pages

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, LaTeX

Given the important role of discrete gauge symmetries in viable models, we discuss these symmetries in intersecting D6-brane trinification model where the ZN symmetry is investigated and its identification is shown., Comment: 6 pages, 0 figures, PTEP (2016)

Using finite discrete group characters and symmetry breaking by hyperflux as well as constraints on top- quark family, we study minimal low energy effective theory following from SU$_{5}\times D_{4}$ models embedded in F-theory with non abelian flux. Matter curves spectrum of the models is obtained from SU$_{5}\times S_{5}$ theory with monodromy $S_{5}$ by performing two breakings; first from symmetric group $S_{5}$ to $S_{4}$ subsymmetry; and next to dihedral $D_{4}$ subgroup. As a consequence, and depending on the ways of decomposing triplets of $S_{4}$, we end with three types of $D_{4}$- models. Explicit constructions of these theories are given and a MSSM- like spectrum is derived., Comment: 48 pages, LaTeX

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 pages

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems., Comment: 24 pages

We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1) $ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint and D3 brane tadpole anomaly of type IIB string on Calabi-Yau threefolds in presence of H$^{RR}$ and H$^{NS}$ fluxes. We also comment on supersymmetry breaking in the particular $\mathcal{N}=2$ $U(1) $ Maxwell theory; and study its interpretation in connection with the tadpole anomaly with extra localized flux sources., Comment: LaTex 37 pages

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO$% _{10}$ models with dihedral $\mathbb{D}_{4}$ discrete symmetry. We first revisit the $\mathbb{S}_{4}$-and $\mathbb{S}_{3}$-models from the discrete group character view, then we extend the construction to $\mathbb{D}_{4}$.\ We find that there are three types of $SO_{10}\times \mathbb{D}_{4}$ models depending on the ways the $\mathbb{S}_{4}$-triplets break down in terms of irreducible $\mathbb{D}_{4}$- representations: $\left({\alpha} \right) $ as $\boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,+}};$ or $\left({\beta}\right) \boldsymbol{\ 1}_{_{+,+}}\oplus \boldsymbol{1}_{_{+,-}}\oplus \boldsymbol{1}_{_{-,-}};$ or also $\left({\gamma}\right) $ $\mathbf{1}_{_{+,-}}\oplus \mathbf{2}_{_{0,0}}$. Superpotentials and other features are also given., Comment: 20 pages, Nuclear Physics B (2015)

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 pages

The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum-classical and quantum-classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined., Comment: 19 pages, To appear in International Journal of Quantum Information

A global measure of quantum correlations for tripartite nonorthogonal states is presented. It is introduced as the overall average of the pairwise correlations existing in all possible partitions. The explicit expressions for the global measure are derived for squared concurrence, entanglement of formation, quantum discord and its geometric variant. As illustration, we consider even and odd three-mode Schr\"odinger cat states based on Glauber coherent states. We also discuss limitations to sharing quantum correlations known as monogamy relations., Comment: 21 pages

A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss., Comment: 21 pages, To appear in Inter. J. Quantum information

The key ingredient of the approach, presented in this paper, is the factorization property of $SU(2)$ coherent states upon splitting or decay of a quantum spin system. In this picture, the even and odd spin coherent states are viewed as comprising two, three or more spin subsystems. From this perspective, we investigate the multipartite quantum correlations defined as the sum of the correlations of all possible bi-partitions. The pairwise quantum correlations are quantified by entanglement of formation and quantum discord. A special attention is devoted to tripartite splitting schemes. We explicitly derive the sum of entanglement of formation for all possible bi-partitions. It coincides with the sum of all possible pairwise quantum discord. The conservation relation between the distribution of entanglement of formation and quantum discord, in the tripartite splitting scheme, is discussed. We show that the entanglement of formation and quantum discord possess the monogamy property for even spin coherent states, contrarily to odd ones which violate the monogamy relation when the the overlap of the coherent states approaches the unity., Comment: 26 pages

The quantum discord is used as measure of quantum correlations for two families of multipartite coherent states. The first family interpolates between generalized GHZ states and generalized Werner states. The second one is an interpolation between generalized GHZ and the ground state of the multipartite quantum system. Two inequivalent ways to split the system in a pair of qubits are introduced. The explicit expressions of quantum quantum discord in multipartite coherent states are derived. Its evaluation uses the Koashi-Winter relation in optimizing the conditional entropy. The temporal evolution of quantum correlations (quantum discord and entanglement) is also discussed.

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl-Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger-Horne-Zeilinger states.

The evolution of pairwise quantum correlations of Bell cat-states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used of the Koashi-Winter relation. A relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

We study intersecting extremal black attractors in non chiral 8D N=1 supergravity with moduli space ((SO(2,N))/(SO(2)\times SO(N)))\times SO(1,1) and work out explicitly the attractor mechanism for various black p-brane configurations with the typical near horizon geometries AdS_{p+2} \times S^{m} \times T^{6-p-m}. We also give the classification of the solutions of the attractor equations in terms of the SO(N-k) subgroups of SO(2)\times SO(N) symmetry of the moduli space as well as their interpretations in terms of both heterotic string on 2-torus and its type IIA dual. Other features such as non trivial SO(1,7) central charges Z_{{\mu}_1...{\mu}_{p}} in 8D N=1 supergravity and their connections to p-form gauge fields are also given. Key Words: 8D Supergravity, Superstring compactifications, Attractor Mechanism, Intersecting Attractors. PACS numbers: 04.70.-s, 11.25.-w, 04.65.+e, 04.70.-s, 04.50.+h, 04.70.Dy, Comment: Latex, 30 pages

Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory, and borrowing ideas from compact geometry of the blowing up of affine ADE singularities, we build a class of local Calabi-Yau threefolds (CY^{3}) extending the local 2-torus model \mathcal{O}(m)\oplus \mathcal{O}(-m)\to T^{2\text{}} considered in hep-th/0406058 to test OSV conjecture. We first study toric realizations of T^{2} and then build a toric representation of X_{3} using intersections of local Calabi-Yau threefolds \mathcal{O}(m)\oplus \mathcal{O}(-m-2)\to \mathbb{P}^{1}. We develop the 2d \mathcal{N}=2 linear \sigma-model for this class of toric CY^{3}s. Then we use these local backgrounds to study partition function of 4d black holes in type IIA string theory and the underlying q-deformed 2d quiver gauge theories. We also make comments on 4d black holes obtained from D-branes wrapping cycles in \mathcal{O}(\mathbf{m}) \oplus \mathcal{O}(\mathbf{-m-2}%) \to \mathcal{B}_{k} with \mathbf{m=}(m_{1},...,m_{k}) a k-dim integer vector and \mathcal{B}_{k} a compact complex one dimension base consisting of the intersection of k 2-spheres S_{i}^{2} with generic intersection matrix I_{ij}. We give as well the explicit expression of the q-deformed path integral measure of the partition function of the 2d quiver gauge theory in terms of I_{ij}., Comment: 36 pages, latex, 9 figures. References added

Using world line fermions $\Upsilon_{\pm}^{m}=\Upsilon_{\pm}^{m}(\tau) $ valued in vector representation of $SO(d,4-d) $ with $d=2,3,4,$ we develop a pure fermionic analog of Penrose twistor construction. First, we show that Fermi antisymmetry requiring $(\Upsilon_{\pm}^{m}) ^{2}=0$ can be solved by using twistor like variables. Then we study the corresponding dual twistor like field action and show that quantum spectrum exhibits naturally 4D $\mathcal{N}=1$ target space supersymmetry. Higher spin world line field solutions of the constraint $(\Pi_{s}^{m}) ^{2}=0$, $s\in \mathbb{Z}$ are also discussed.

We use local mirror symmetry to study a class of local Calabi-Yau super-manifolds with bosonic sub-variety V_b having a vanishing first Chern class. Solving the usual super- CY condition, requiring the equality of the total U(1) gauge charges of bosons \Phi_{b} and the ghost like fields \Psi_{f} one \sum_{b}q_{b}=\sum_{f}Q_{f}, as \sum_{b}q_{b}=0 and \sum_{f}Q_{f}=0, several examples are studied and explicit results are given for local A_{r} super-geometries. A comment on purely fermionic super-CY manifolds corresponding to the special case where q_{b}=0, \forall b and \sum_{f}Q_{f}=0 is also made.\bigskip, Comment: 17 pages

In this paper, we provide a general classification of supersymmeric QFT$_{4}$s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super QFT$_{4}$s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT$_{4}$s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made., Comment: 25 pages, 2 figures