Related papers: Unit Quaternions and the Bloch Sphere
We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements…
The combination of space inversion and time reversal symmetries result in doubly-degenerate Bloch states with opposite spin. Many lattices with these symmetries can be constructed by combining a noncentrosymmetric potential (lacking this…
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining Triada of Malevich's squares. The three triangle…
It is very important to understand if a qutrit can be visualized in a 3-dimensional Bloch sphere. In this work, a mathematical model for performing this operation is presented.
A quantum spin-1/2, and its associated su(2) algebra of Pauli spin matrices are familiarly linked to Clifford algebra and quaternions. Somewhat more loosely, we develop connections between the su(4) algebra of two spins and of its…
Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated,…
In this paper, we prove that time-like constant slope surfaces can be reparametrized by using rotation matrices corresponding to unit time-like split quaternions and homothetic motions. Afterwards we give some examples to illustrate our…
In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…
The Majorana's stellar representation, which represents the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, provides an intuitive way to study a physical system with high dimensional projective…
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state…
We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are…
Rotations in 3 dimensional space are equally described by the SU(2) and SO(3) groups. These isomorphic groups generate the same 3D kinematics using different algebraic structures of the unit quaternion. The Hopf Fibration is a projection…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
Quaternion (Q-) mathematics formally contains many fragments of physical laws; in particular, the Hamiltonian for the Pauli equation automatically emerges in a space with Q-metric. The eigenfunction method shows that any Q-unit has an…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
In quantum computation and information science, the geometrical representations based on the Bloch sphere representation for transformations of two state systems have been traditionally used. While this representation is very useful for the…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…