Related papers: The Qutrit Bloch Sphere
Three unit spheres were used to represent the two-qubit pure states. The three spheres are named the base sphere, entanglement sphere, and fiber sphere. The base sphere and entanglement sphere represent the reduced density matrix of the…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
In this research, we introduce an algorithm that produces what appears to be a new mathematical object as a consequence of projecting the \( n \)-dimensional \( Z \)-curve onto an \( n \)-dimensional sphere. The first part presents the…
A list of known quantum spheres of dimension one, two and three is presented.
We establish a surgery formula for 3-dimensional Seiberg-Witten monopoles under (+1) Dehn surgery on a knot in a homology 3-sphere. (substantial revision)
In this paper we propose a new version for the noncommutative superspace in 3D. This version is shown to be convenient for performing quantum calculations. In the paper, we use the theory of the chiral superfield as a prototype for possible…
It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.
The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any…
We calculate the Witt ring of the real sphere.
We study the problem of information masking through nonzero linear operators that distribute information encoded in single qubits to the correlations between two qubits. It is shown that a nonzero linear operator cannot mask any nonzero…
Some features of a parametrized space of orbits in the Schwarzschild geometry are described.
In this paper, we study the possibility of model building of cyclic universe with Quintom matter in the framework of Loop Quantum Cosmology. After a general demonstration, we provide two examples, one with double-fluid and another…
We study the Erdos distance conjecture on the unit sphere in three dimensions using Fourier analytic methods.
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
We introduce a visual representation of qubits to assist in explaining quantum computing to a broad audience. The representation follows from physical devices that we developed to explain superposition, entanglement, measurement, phases,…
The observation of neutron interference by using a crystal interferometer having a separate analyser opens the way to the construction and operation of interferometers with vast arm separation and length. Setting the design specifications…
We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized,…
We develop an algorithm capable of imaging a three-dimensional object given a collection of two-dimensional images of that object that are significantly influenced by the curvature of the Ewald sphere. These two-dimensional images cannot be…
Astronomical data take on a multitude of forms -- catalogs, data cubes, images, and simulations. The availability of software for rendering high-quality three-dimensional graphics lends itself to the paradigm of exploring the incredible…