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Unconditionally secure bit commitment is forbidden by quantum mechanics. Weextend this no-go theorem to continuous-variable protocols where both playersare restricted to use Gaussian states and operations, which is a reasonableassumption in current-state optical implementations. Our Gaussian no-go theoremalso provides a natural counter-example to a conjecture that quantum mechanicscan be rederived from the assumption that key distribution is allowed while bitcommitment is forbidden in Nature.

Strong no-go theorem for Gaussian quantum bit commitment