  Among the known resources of quantum metrology, one of the most practical and
efficient is squeezing. Squeezed states of atoms and light improve the sensing
of the phase, magnetic field, polarization, mechanical displacement. They
promise to considerably increase signal-to-noise ratio in imaging and
spectroscopy, and are already used in real-life gravitational-wave detectors.
But despite being more robust than other states, they are still very fragile,
which narrows the scope of their application. In particular, squeezed states
are useless in measurements where the detection is inefficient or the noise is
high. Here, we experimentally demonstrate a remedy against loss and noise:
strong noiseless amplification before detection. This way, we achieve
loss-tolerant operation of an interferometer fed with squeezed and coherent
light. With only 50\% detection efficiency and with noise exceeding the level
of squeezed light more than 50 times, we overcome the shot-noise limit by 6~dB.
Sub-shot-noise phase sensitivity survives up to 87\% loss. Application of this
technique to other types of optical sensing and imaging promises a full use of
quantum resources in these fields.
