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In standard coherent state teleportation with shared two-mode squeezed vacuum(TMSV) state there is a trade-off between the teleportation fidelity and thefidelity of estimation of the teleported state from results of the Bellmeasurement. Within the class of Gaussian operations this trade-off is optimal,i.e. there is not a Gaussian operation which would give for a given outputfidelity a larger estimation fidelity. We show that this trade-off can beimproved by up to 2.77% if we use a suitable non-Gaussian operation. Thisoperation can be implemented by the standard teleportation protocol in whichthe shared TMSV state is replaced with a suitable non-Gaussian entangled state.We also demonstrate that this operation can be used to enhance the transmissionfidelity of a certain noisy channel.Comment: submitted to Physical Review A, new results added, 7 pages, 4 figure

Minimal disturbance measurement for coherent states is non-Gaussian