Representations of the qubit states (original) (raw)

Abstract

In this article we present the relevant characteristics of the qubit and its various representations and descriptions. We give both the state vector and matrix density formulations and follow a proper graphic illustration of the qubit states and transformations. Besides the new Bloch Sphere representations, a new Cartesian Sphere representation is proposed for both state vector and matrix density formulations. In this representation the fundamental states are considered in the xOy plane and imaginary combinations of the fundamental states are placed on a direction orthogonal to this plane. This representation is useful for the qubits identified in quantum systems with certain symmetry or asymmetry.

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