Revisiting Boole Equation in the Quantum Context

In this work we try to clarify the fundamental relationship between bits and qubits, starting from very simple George Boole equation. We derive a generic and compact expression for basis vectors of qubit which can be useful in further applications. We also derive a generic form for the projection operator in the quantum information space. The results are also extended to higher d-level cases of qutrits and qudits.