Related papers: The Qutrit Bloch Sphere
Spectral triples on the q-deformed spheres of dimension two and three are reviewed.
There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…
A general protocol in Quantum Information and Communication relies in the ability of producing, transmitting and reconstructing, in general, qunits. In this letter we show for the first time the experimental implementation of these three…
This paper reviews recent attempts to describe the two- and three-qubit Hilbert space geometries with the help of Hopf fibrations. In both cases, it is shown that the associated Hopf map is strongly sensitive to states entanglement content.…
The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.
Block spin renormalization group is the main tool used in our program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It generates operators, like the fluctuation…
A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [M. Boyer, R. Liss, T.…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
The squircle is an intermediate shape between the square and the circle. In this paper, we examine and discuss equations for different types of squircles. We then build upon these 2D shapes to come-up with various 3D surfaces based on…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…
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…