In some experiments as the modified Stern-Gerlach experiment or the double slit experiment you have to admit that the system under study is in two (or more) states at the same time. See this video, for example, for the modified Stern-Gerlach:
The key question is: with this modification of the $SG_z$ device (the "hardness box"), which path do the particles follow? If an electro went through path 1, its statistic after $SG_x$ should be 50/50. The same for path 2. So a reasonable hypothesis to bear in mind is that the state "black" (or $|\to \rangle$) is a superposition of "path 1" and "path 2". Another perspective (or is it the same?) is to consider that the particle went through both paths at the same time: like two parallel universes that get merged together at the end...
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Author of the notes: Antonio J. Pan-Collantes
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