  Knowing about optimal quantum measurements is important for many applications
in quantum information and quantum communication. However, deriving optimal
quantum measurements is often difficult. We present a collection of results for
minimum-cost quantum measurements, and give examples of how they can be used.
Among other results, we show that a minimum-cost measurement for a set of given
pure states is formally equivalent to a minimum-error measurement for mixed
states of those same pure states. For pure symmetric states it turns out that
for a certain class of cost matrices, the minimum-cost measurement is the
square-root measurement. That is, the optimal minimum-cost measurement is in
this case the same as the minimum-error measurement. Finally, we consider
sequences of individual ``local" systems, and examine when the global
minimum-cost measurement is a sequence of optimal local measurements. We also
consider an example where the global minimum-cost measurement is, perhaps
counter-intuitively, not a sequence of local measurements, and discuss how this
is related to related to the Pusey-Barrett-Rudolph argument for the nature of
the wave function.
