  We consider the hypothetical quantum network case where Alice wishes to
transmit one qubit of information (specifically a pure quantum state) to $M$
parties, where $M$ is some large number. The remote receivers locally perform
single qubit quantum state tomography on the transmitted qubits in order to
compute the quantum state within some error rate (dependent on the tomography
technique and number of qubits used). We show that with the use of an
intermediate optimal symmetric universal quantum cloning machine (between Alice
and the remote receivers) as a repeater-type node in a hypothetical quantum
network, Alice can send significantly fewer qubits compared to direct
transmission of the message qubits to each of the $M$ remote receivers. This is
possible due to two properties of quantum cloning. The first being that single
qubit quantum clones retain the same angle, in the Bloch sphere representation,
as the initial quantum state. This means that if the mixed state of the quantum
clone can be computed to high enough accuracy, the pure quantum state can be
computed by extrapolating that vector to the surface of the Bloch sphere. The
second property is that the state overlap of approximate quantum clones, with
respect to the original pure quantum state, quickly converges (specifically for
$1 \rightarrow M$ the limit of the fidelity as M goes to infinity is
$\frac{2}{3}$). This means that Alice can prepare a constant number of qubits
(which are then passed through the quantum cloning machine) in order to achieve
a desired error rate, if $M$ is large enough. Combined, these two properties
mean that for large $M$, Alice can prepare orders of magnitude fewer qubits in
order to achieve the same single qubit transmission accuracy compared to the
naive direct qubit transmission approach.
