  Quantum technology promises revolutionary advantages in information
processing and transmission compared to classical technology; however,
determining which specific resources are needed to surpass the capabilities of
classical machines often remains a nontrivial problem. To address such a
problem, one first needs to establish the best classical solutions, which set
benchmarks that must be beaten by any implementation claiming to harness
quantum features for an enhanced performance. Here we introduce and develop a
self-contained formalism to obtain the ultimate, generally probabilistic
benchmarks for quantum information protocols including teleportation and
approximate cloning, with arbitrary ensembles of input states generated by a
group action, so-called Gilmore-Perelomov coherent states. This allows us to
construct explicit fidelity thresholds for the transmission of multimode
Gaussian and non-Gaussian states of continuous variable systems, as well as
qubit and qudit pure states drawn according to nonuniform distributions on the
Bloch hypersphere, which accurately model the current laboratory facilities.
The performance of deterministic classical procedures such as square-root
measurement strategies is further compared with the optimal probabilistic
benchmarks, and the state-of-the-art performance of experimental quantum
implementations against our newly derived thresholds is discussed. This work
provides a comprehensive collection of directly useful criteria for the
reliable certification of quantum communication technologies.
