  We consider the problem of reproducing one quantum measurement given the
ability to perform another. We give a general framework and specific protocols
for this problem. For example, we show how to use available "imperfect" devices
a small number of times to implement a target measurement with average error
that drops off exponentially with the number of imperfect measurements used. We
hope that could be useful in near-term applications as a type of lightweight
error mitigation of the measuring devices. As well as the view to practical
applications, we consider the question from a general theoretical perspective
in the most general setting where both the available and target measurements
are arbitrary generalised quantum measurements. We show that this general
problem in fact reduces to the ability to reproduce the statistics of
(complete) von Neumann measurements, and that in the asymptotic limit of
infinitely many uses of the available measurement, a simple protocol based upon
`classical cloning' can perfectly achieve this task. We show that
asymptotically all (non-trivial) quantum measurements are equivalent. We also
study optimal protocols for a fixed number of uses of the available
measurement. This includes, but is not limited to, improving both noisy and
lossy quantum measurements. Furthermore, we show that, in a setting where we
perform multiple measurements in parallel, we can achieve finite-rate
measurement reproduction, by using block-coding techniques from classical
information theory. Finally, we show that advantages can also be gained by
making use of probabilistic protocols.
