Quoins versus Coins

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Human monkeys are used to thinking about the problem of
choosing from a set of objects according to some desired, biased, probability
distribution. Just think about how you chose your partner(s). Even when it is
easy for you to do such a sampling, it can be difficult to do a quantum
sampling (Q-Sampling) of the same distribution. By Q-Sampling I mean the
creation of a coherent superposition of states of such objects whose amplitudes
are the (square roots of) of the specified distribution. In this talk I will
discuss what we do know about this problem, why it is interesting, and will
discuss how it can let us achieve tasks with quantum information that are
provably impossible classically.