In the classical world one can construct two identical systems which have
identical behavior and give identical measurement results. We show this to be
impossible in the quantum domain. We prove that after the same quantum
measurement two different quantum systems cannot yield always identical
results, provided the possible measurement results belong to a non orthogonal
set. This is interpreted as quantum uniqueness - a quantum feature which has no
classical analog. Its tight relation with objective randomness of quantum
measurements is discussed.Comment: Presented at 4th Feynman festival, June 22-26, 2009, in Olomouc,
Czech Republic
