Spinors and Bloch sphere

Spinors and Bloch vectors are two views of single-qubit state information.

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Spinor form

|psi> = alpha|0> + beta|1>
|alpha|^2 + |beta|^2 = 1

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Bloch mapping

A normalized spinor maps to a point on the Bloch sphere:

n = (sin(theta)cos(phi), sin(theta)sin(phi), cos(theta))

Global phase does not change the Bloch point.