  Quantum communication has been leading the way of many remarkable theoretical
results and experimental tests in physics. In this context, quantum
communication complexity (QCC) has recently drawn earnest research attention as
a tool to optimize the amounts of transmitted qubits and energy that are
required to implement distributed computational tasks. On this matter, we
introduce a novel multi-user quantum fingerprinting protocol that is ready to
be implemented with existing technology. Particularly, we extend to the
multi-user framework a well-known two-user coherent-state fingerprinting
scheme. This generalization is highly non-trivial for a twofold reason, as it
requires not only to extend the set of protocol rules but also to specify a
procedure for designing the optical devices intended for the generalized
protocol. Much of the importance of our work arises from the fact that the
obtained QCC figures of merit allow direct comparison with the best-known
classical multi-user fingerprinting protocol, of significance in the field of
computer technologies and networking. Furthermore, as one of the main
contributions of the manuscript, we deduce innovative analytical upper bounds
on the amount of transmitted quantum information that are even valid in the
two-user protocol as a particular case. Ultimately, comparative results are
provided to contrast different protocol implementation strategies and,
importantly, to show that, under realistic circumstances, the multi-user
protocol can achieve tasks that are impossible by using classical communication
alone. Our work provides relevant contributions towards understanding the
nature and the limitations of quantum fingerprinting and, on a broader scope,
also the limitations and possibilities of quantum-communication networks
embracing a node that is accessed by multiple users at the same time.
