If I construct a set of qubit gates, say {G(adsbygoogle = window.adsbygoogle || []).push({}); _{1}, G_{2}... G_{k}... G_{n}}, that can act on a state |ψ>, what does it mean for the set of states G_{k}|ψ> to span the Bloch sphere?

As an example, take the set {G_{1}, G_{2}, G_{3}, G_{4}} = { I, X_{ π/2 }, Y_{ π/2}, X_{π}}

Here, X_{ π/2 }denotes a π/2 rotation about the x-axis, Y_{ π/2 }denotes a π/2 rotation about the y-axis, and so on.

The set of states |ψ_{k}>= G_{k}|ψ>, is said to span the Bloch sphere. But I'm having trouble understanding what this really means.

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# I What does it mean to span the Bloch sphere?

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