Representing quantum spins in different coordinate systems for modelling rigid body orientation

Abstract Various methods for representing the spatial orientation and rotation of objects are presented and compared with the quantum bit state representation. By contrasting spherical, Euler angle, quaternion, and quantum spin coordinate systems, this work highlights important concepts regarding the rotation axis of the X gate. Several ambiguities and incomplete definitions associated with the qubit state representation are discussed, such as the spin around the qubit itself and the explanation of the considered rotation angles and signs. A mathematical analysis of the physical meaning of each eigenstate is provided along with a new comprehensive and meaningful YPR-based 3D representation of a qubit state.