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| CATEGORIES ABOUT BLOCH SPHERE | |
| quantum mechanics | |
| projective geometry | |
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Bloch sphere In Quantum Mechanics , the Bloch sphere is a geometrical representation of the Pure State space of a 2-level quantum mechanical system. Alternatively, it is the pure state space of a 1 Qubit quantum register. The Bloch sphere is actually geometrically a sphere and the correspondence between elements of the Bloch sphere and pure states can be explicitly given. Quantum mechanics is mathematically formulated in Hilbert Space . The space of pure states of a quantum system is given by the rays in the Hilbert space. The space of rays in any Vector Space is a Projective Space , and in particular, the space of rays in a two dimensional Hilbert space is the Complex Projective Line , which is isomorphic to a sphere. | ||
| :<math> \psi Angle | \cos heta \, 0
angle + e^{i \phi} \sin heta \,1
angle </math> |
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