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