If we have vertical linearly polarized light and if we put it through a polarizing filter oriented at 45 to the vertical, then only half of the light passes through.
I am able to intuitively grasp this fact as photons of vertically polarized light may exist in a superposition of being in two diagonally polarized and mutually perpendicular states, for which the amplitudes interfere. Thus upon interacting with the filter half of the photons pass through.
But if we subsequently pass this light through another filter which is oriented horizontally, still half of this light will pass through.
Why does this happen? Doesn't the fact that it passed through the first filter mean that it is oriented diagonally without uncertainty? How can it, after passing through the first filter, still exist in superposition of two states? Wouldn't the act of passing it through a filter disturb this superposition and force it to occupy one definite state?
