  A communication protocol based on a Gaussian modulation of squeezed states in
a single quadrature and measured via homodyne detection can completely
eliminate information leakage to an eavesdropper in a pure-loss channel.
However, the asymmetry of the protocol with respect to the quadratures of light
presents security issues and the eavesdropper's information is not necessarily
minimized for general asymmetric attacks. Here, we perform asymptotic security
analysis of the asymmetric protocol against general asymmetric collective
attacks and bound the eavesdropper's information via the Heisenberg uncertainty
principle. The bound is not tight and therefore, we symmetrize the protocol in
a heralding way, discarding the issues of asymmetry altogether. Our proposed
heralding protocol asymptotically eliminates information leakage in a pure-loss
channel and minimizes leakage in a noisy channel.
