  Distributing entangled pairs is a fundamental operation required for many
quantum information science and technology tasks. In a general entanglement
distribution scheme, a photonic pulse is used to entangle a pair of remote
quantum memories. Most applications require multiple entangled pairs between
remote users, which in turn necessitates several photonic pulses (single
photons) being sent through the channel connecting those users. Here we present
an entanglement distribution scheme using only a single photonic pulse to
entangle an arbitrary number of remote quantum memories. As a consequence the
spatial temporal resources are dramatically reduced. We show how this approach
can be simultaneously combined with an entanglement purification protocol to
generate even higher fidelity entangled pairs. The combined approach is faster
to generate those high quality pairs and requires less resources in terms of
both matter qubits and photons consumed. To estimate the efficiency of our
scheme we derive a normalized rate taking into account the raw rate at which
the users can generate purified entangled pairs divided by the total resources
used. We compare the efficiency of our system with the Deutsch protocol in
which the entangled pairs have been created in a traditional way. Our scheme
outperforms this approach both in terms of generation rate and resources
required. Finally we show how our approach can be extended to more general
error correction and detection schemes with higher normalized generation rates
naturally occurring.
