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“In an experiment like that in figure a, where a photon is fired
at a half-silvered mirror, it can be shown that the photon does not actually
split by verifying that if one detector registers a signal, then no other
detector does.  With this piece of information, one might think that
any given photon travels either vertically or horizontally, randomly choosing
between the two paths.  However, quantum mechanics predicts that the
photon actually travels both paths simultaneously, collapsing down to one
path only upon measurement.  This effect, known as single-particle
interference, can be better illustrated in a slightly more elaborate
experiment, outlined in figure b below:

 

 




(Figure taken from a paper
by Deutsch and Ekert)
In this experiment, the photon first
encounters a half-silvered mirror, then a fully silvered mirror, and finally
another half-silvered mirror before reaching a detector, where each half-silvered
mirror introduces the probability of the photon traveling down one path
or the other.  Once a photon strikes the mirror along either of the
two paths after the first beam splitter, the arrangement is identical to
that in figure a, and so one might hypothesize that the photon will
reach either detector A or detector B with equal probability.  However,
experiment shows that in reality this arrangement causes detector A to
register 100% of the time, and never at detector B! 
How can this be?


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