Spin passing through wire loop

Consider a spin-1/2 particle passing through a wire loop with a light bulb in series:

Screen Shot 2018-04-07 at 9.56.45 PM.png

The spin produces a magnetic moment and therefore a magnetic field, which can induce current in the loop due to changing flux. For a pure upwards-pointing spin \lvert\uparrow\rangle (shown above), we have an increasing upwards flux before it enters and a decreasing flux afterwards, so the light bulb turns on before and after entering the loop. For \lvert\downarrow\rangle the flux is reversed but the light bulb still turns on at the same times.

Now let the spin part of the wavefunction be \frac{1}{\sqrt{2}}(\lvert\uparrow\rangle + \lvert\downarrow\rangle). Does the light bulb turn on?


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