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Quantum technology promises revolutionary advantages in informationprocessing and transmission compared to classical technology; however,determining which specific resources are needed to surpass the capabilities ofclassical machines often remains a nontrivial problem. To address such aproblem, one first needs to establish the best classical solutions, which setbenchmarks that must be beaten by any implementation claiming to harnessquantum features for an enhanced performance. Here we introduce and develop aself-contained formalism to obtain the ultimate, generally probabilisticbenchmarks for quantum information protocols including teleportation andapproximate cloning, with arbitrary ensembles of input states generated by agroup action, so-called Gilmore-Perelomov coherent states. This allows us toconstruct explicit fidelity thresholds for the transmission of multimodeGaussian and non-Gaussian states of continuous variable systems, as well asqubit and qudit pure states drawn according to nonuniform distributions on theBloch hypersphere, which accurately model the current laboratory facilities.The performance of deterministic classical procedures such as square-rootmeasurement strategies is further compared with the optimal probabilisticbenchmarks, and the state-of-the-art performance of experimental quantumimplementations against our newly derived thresholds is discussed. This workprovides a comprehensive collection of directly useful criteria for thereliable certification of quantum communication technologies.

Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states