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Returning to the communications example: Starting from 256-QAM,
if you throw away the v2 axis in phase space, and collapse
everything down onto the v1 axis, you would be throwing away
something like 15/16ths of the available phase space. Not a
good idea.
This is a fairly good shibboleth for identifying experimental
physicists: If you ask somebody to measure an AC signal, the
physicist will instinctively reach for a lockin amplifier, in
situations where an ordinary mortal would reach for a voltmeter.