  Entanglement and quantum communication are paradigmatic resources in quantum
information science leading to correlations between systems that have no
classical analogue. Correlations due to entanglement when communication is
absent have for long been studied in Bell scenarios. Correlations due to
quantum communication when entanglement is absent have been studied extensively
in prepare-and-measure scenarios in the last decade. Here, we set out to
understand and investigate correlations in scenarios that involve both
entanglement and communication, focusing on entanglement-assisted
prepare-and-measure scenarios. In a recent companion paper [arXiv:2103.10748],
we investigated correlations based on unrestricted entanglement. Here, our
focus is on scenarios with restricted entanglement. We establish several
elementary relations between standard classical and quantum communication and
their entanglement-assisted counterparts. In particular, while it was already
known that bits or qubits assisted by two-qubit entanglement between the sender
and receiver constitute a stronger resource than bare bits or qubits, we show
that higher-dimensional entanglement further enhance the power of bits or
qubits. We also provide a characterisation of generalised dense coding
protocols, a natural subset of entanglement-assisted quantum communication
protocols, finding that they can be understood as standard quantum
communication protocols in real-valued Hilbert space. Though such dense coding
protocols can convey up to two bits of information, we provide evidence,
perhaps counter-intuitively, that resources with a small information capacity,
such as a bare qutrits, can sometimes produce stronger correlations. Along the
way we leave several conjectures and conclude with a list of interesting open
problems.
