Bloch SphereΒΆ
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The Bloch sphere is used to represent the state of two-level systems.
It is, in fact, the visualization of vectors of a complex Hilbert space of dimension 2 (\(\mathbb C^2\) space), in contrast to real spaces, that we are familiar with and easy to interpret.
The two vectors \(\ket{0}\) and \(\ket{1}\) of a chosen basis are represented on the z-axis.
While the x- and y-axis represent the following superpositions of the basis vectors:
x-axis: \(\ket{0} \pm \ket{1}\)
y-axis: \(\ket{0} \pm i \ket{1}\)
Complements