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Jun 7, 2012 at 9:40 comment added Carl Brannen To have an interference requires that the rotated and non rotated particles begin in a coherent state. Then you can use the density matrix form for them, but it has to be the two particle density matrix. So what you're doing is rotating one particle while not rotating the other. The result is indeed observable, one way of describing it is as a quantum phase, a topological phase, or Berry-Pancharatnam phase. But for a single particle, or a pair of particles, or any number of particles, rotating them all (i.e. rotating the system) by 360 degrees is not detectable.
Jun 6, 2012 at 20:15 comment added Emilio Pisanty However, relative phases between different pasts of a system will produce physical results. If you rotate one particle through 360$^\circ$, then you can interfere it against a non-rotated particle to get a shifted pattern. The overall density matrix will reflect this: all the (inter-particle) coherences will change sign.
Feb 10, 2011 at 11:16 history answered Carl Brannen CC BY-SA 2.5