Related papers: On the SU(3) parametrization of qutrits
Remarkably simple closed-form expressions for the elements of the groups SU(n), SL(n,R), and SL(n,C) with n=2, 3, and 4 are obtained using linear functions of biquaternions instead of n x n matrices. These representations do not directly…
We propose two simple models for the quark mass matrices which may be implemented through an S3 x Z2 symmetry in a supersymmetric context. Each model has eight parameters and, therefore, makes two independent predictions for the quark…
Let $X$, $Y$ be sets and let $\Phi$, $\Psi$ be mappings with domains $X^{2}$ and $Y^{2}$ respectively. We say that $\Phi$ and $\Psi$ are combinatorially similar if there are bijections $f \colon \Phi(X^2) \to \Psi(Y^{2})$ and $g \colon Y…
The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then…
We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence…
We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…
We examine possible assignments for known mesons to the predicted ground-state q bar q multiplets in the U~(12)_SF-classification scheme of hadrons, based on their observed properties. The masses of missing members of the ground-state…
We impose partial-wave unitarity on $2 \to 2$ tree-level scattering processes to derive constraints on the dimensions of large scalar and fermionic multiplets of arbitrary gauge groups. We apply our results to scalar and fermionic…
In this note we comment on yet another way of describing metric of quantum states with the Lorentzian signature. For this, we consider the metric of quantum states and make successive transformations, exploiting the relationship between S3…
A parameterization for the power sums of GL(m|n) type quantum (super)matrix is obtained in terms of it's spectral values.
A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated. The group--subgroup in question is that of the…
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit…
Group theoretical factors from GUT symmetry breaking can lead to predictions for the ratios of quark and lepton masses at the unification scale. Due to supersymmetric (SUSY) threshold corrections the viability of such predictions can depend…
We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of qubit states and observables is formally equivalent to the…
Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…
As is well-known, Trinification, \ie, the extension of the Standard Model (SM) to $[SU(3)]^3=SU(3)_c\times SU(3)_L\times SU(3)_R$ as occurs in $E_6$ models, allows for a partial unification of the gauge forces even though quarks and leptons…
We consider local unitary invariants and entanglement monotones for the mixed two qutrit system. Character methods for the local SU(3)xSU(3) transformation group are used to establish the count of algebraically independent polynomial…
We propose novel mixed states in two qubits, ``maximally entangled mixed states'', which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
In the light of several recent analyses pointing towards texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and…