  While the no-cloning theorem forbids the perfect replication of quantum
information, it is sometimes possible to produce large numbers of replicas with
vanishingly small error. This phenomenon, known as quantum superreplication,
can take place both for quantum states and quantum gates. The aim of this paper
is to review the central features of quantum superreplication, providing a
unified view on the existing results. The paper also includes new results. In
particular, we show that, when quantum superreplication can be achieved, it can
be achieved through estimation, up to an error vanishing with a power law.
Quantum strategies still offer an advantage for superreplication, in that they
allow for an exponentially faster reduction of the error. Using the relation
with estimation, we provide i) an alternative proof of the optimality of the
Heisenberg scaling of quantum metrology, ii) a strategy to estimate arbitrary
unitary gates with Heisenberg scaling, up to a logarithmic overhead, and iii) a
protocol that generates M nearly perfect copies of a generic pure state with a
number of queries to the corresponding unitary gate scaling as the square root
of M. Finally, we point out that superreplication can be achieved using
interactions among k systems, provided that k is large compared to square of
the ratio between the numbers of input and output copies.
