09 - Understanding the Bloch Sphere and Qubit Geometry

The Bloch sphere provides a geometric framework to visualize the state of a single quantum bit. Pure qubit states, from classical poles like zero and one to equatorial superpositions, map directly onto the surface of a three-dimensional sphere. Unitary quantum logic gates, including the Pauli and Hadamard gates, operate as rigid spatial rotations that transform these states. Furthermore, the sphere captures quantum phase along its equator and illustrates how environmental decoherence drags pure states into the interior as mixed states. While single-qubit behavior maps cleanly to this geometry, multi-qubit entanglement lies beyond the limits of a single three-dimensional sphere. Sources [1]    • From Poincaré sphere  (Bloch sphere) to Pr...   [2] https://baldwinlab.chem.ox.ac.uk/reso... [3]    • The Poincaré Sphere  to represent polarize...   [4] https://pubs.aip.org/aip/jap/article/... [5] https://spie.org/publications/spie-pu... [6] https://pubs.aip.org/aip/jap/article-... [7] https://spindynamics.org/relaxation_e...