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Quantum mechanical effects of single particles can affect the collective plasmon behaviors substantially. In this work, the quantum control of plasmon excitation and propagation in graphene is demonstrated by adopting the variable quantum transmission of carriers at Heaviside potential steps as a tuning knob. First, the plasmon reflection is revealed to be tunable within a broad range by varying the ratio γ between the carrier energy and potential height, which originates from the quantum mechanical effect of carrier propagation at potential steps. Moreover, the plasmon excitation by free-space photos can be regulated from fully suppressed to fully launched in graphene potential wells also through adjusting γ, which defines the degrees of the carrier confinement in the potential wells. These discovered quantum plasmon effects offer a unified quantum-mechanical solution toward ultimate control of both plasmon launching and propagating, which are indispensable processes in building plasmon circuitry. [ABSTRACT FROM AUTHOR]