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A single qubit is represented with a bloch sphere and implemented on an electron with only two energy values from lots of them.
So, I am confused about why an energy range is represented as a vector on a sphere, and also with the relation between the spin vector from Dirac or Pauli equation and the Bloch Vector. I think the first is a SO3 vector on real space, and the bloch one is SU2 on internal space. So Bloch sphere is not the real spin? When we rotate that spin with microwaves are we rotating the real spin?

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    $\begingroup$ Electrons are spin 1/2 systems, which have two basis states (up and down). The Bloch sphere represents a system with two basis states, so it certainly does represent electrons. i'm not super great with quantum mechanics, but it seems you may be confused in that the energy levels doesn't necessarily align with the spin levels? an electron can be in many many different energy levels in an atom, but has two in the stern gerlach experiment because the two levels align with the two possible spin states. regardless, you don't really need to worry about its energy states, only its two spin states. $\endgroup$
    – tpws
    Aug 7, 2023 at 21:19

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