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How to find out whether it is a positive or negative $\pi$ phrase between 00 and 11 from q-Sphere diagram?

qshere

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The phase corresponding to the color of state $|11\rangle$ is $e^{i \pi}= -1$. So, it is a negative phase.

Generally, you plug in whatever angle the color of the state corresponds to into $e ^{i \theta}$ to get the phase of the state.

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As per @epelaaez's answer: the node color indicates the relative phase. However, there is a subtle point here.

As stated in this page, if you run this code snippet

Ψ = [8 / 17, 0, 0, 15j / 17]
plot_state_qsphere(Ψ, show_state_phases = True)

the result will be

enter image description here

You can see that $|11⟩$ is displayed with phase = $0$ although it has a phase greater than zero. On the other hand, $|00⟩$ is displayed with a phase while it does not have one! This is because plot_state_qsphere function removes the phase from the term with maximum probability, and normalizes the phases of other terms accordingly.

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