Related papers: Unit Quaternions and the Bloch Sphere
On the basis of the first principles we derive the Barut-Wilson-Fushchich second-order equation in the (1/2,0)+(0,1/2) representation. Then we discuss the possibility of the description of various mass and spin states in such a framework.
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
A non-abelian spin liquid in triangular lattice spin-1 systems was recently formulated in the form of continuum field theory [T. Grover, and T. Senthil, Phys. Rev. Lett. 107, 077203 (2011); Cenke Xu, A.W.W. Ludwig, arXiv:1012.5671]. It has…
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a…
Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In…
We propose an alternative approach for the construction of the unitary matrix which performs generalized unitary rotations of the system consisting of independent identical subsystems (for example spin system). This matrix, when applied to…
We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous…
A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three time-like coordinates, we have been able to consistently recover a suitable formulation of…
The geometry of the generalized Bloch sphere $\Omega_3$, the state space of a qutrit, is studied. Closed form expressions for $\Omega_3$, its boundary $\partial \Omega_3$, and the set of extremals $\Omega_3^{\rm ext}$ are obtained by use of…
We propose a state estimation scheme for spins, using a modified setup of the Stern-Gerlach experiment, in which a beam of neutral spin-1/2 point particles interacts with a quadrupolar magnetic field. The proposed linear inversion…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
The modified Navier-Stokes equation describing the velocity field in the superfluid quantum space is loaded by the external Lorentz force introducing electromagnetic fields. In order to open the path for getting the \Schrodinger-Pauli…
The Bloch sphere provides an elegant way of visualizing a qubit. Analogous representation of the simplest composite state of two-qubits has attracted significant attention. Here we present a detailed mathematical analysis of the real-matrix…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
The Cartan's equations definig simple spinors (renamed pure by C. Chevalley) are interpreted as equations of motion in momentum spaces, in a constructive approach in which at each step the dimesions of spinor space are doubled while those…
Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. In order to probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…