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

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

Building SO10_{10}- models with D4\mathbb{D}_{4} symmetry

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

Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy

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 Informatio