The Analysis of Quantum Qutrit Entanglements in a Qutrit Based Hyper-Sphere in Terms of Gluing and Combining Products

Abstract

In this research the aim is to analyze quantum qutrit entanglements in a new perspective in terms of the reflection of n-dimensional sphere which can be depicted as the set of points equidistant from a fixed central point in three dimensional Euclidian Space which has also real and imaginary dimensions, that can also be depicted similarly as a two unit spheres having same centre in a dome-shaped projection. In order to analyze quantum qutrit entanglements: i-a new type of n dimensional hyper-sphere which is the extend version of Bloch Sphere to hyper-space, is defined ii-new operators and products such as rotation operator, combining and gluing products in this space are defined, iii-the entangled states are analyzed in terms of those products in order to reach a general formula to depict qutrit entanglements and some new patterns between spheres for the analysis of entanglement for different routes in a more simple way in a four dimensional time independent hypersphere.