  Squeezed states of light have been improving the sensitivity of
gravitational-wave observatories and are nonclassical resources of quantum
cryptography and envisioned photonic quantum computers. The higher the squeeze
factor is, the higher is the quantum advantage. Almost all applications of
squeezed light require multi-path optical interference, whose unavoidable
imperfections introduce optical loss, degrade the squeeze factor, as well as
the quantum advantage. Here, for the first time, we experimentally demonstrate
the distillation of Gaussian squeezed states that suffered from Gaussian photon
loss. Our demonstration already involves two distillation steps. The first step
improved the squeeze factor from 2.4 dB to 2.8 dB by the subtraction of two
photons. The second step improved the value from 2.8 dB to 3.4 dB by a
Gaussification protocol. It was realised on data measured at different times
via an 8-port balanced homodyne detector and via data post-processing. The
number of distillation steps can be increased by longer data sampling times,
without additional hardware. We propose and discuss the application to quantum
cryptography and photonic quantum computers.
