  Entangled microwave photons form a fundamental resource for quantum
information processing and sensing with continuous variables. We use a low-loss
Josephson metamaterial comprising superconducting, non-linear, asymmetric
inductive elements to generate frequency-entangled photons from vacuum
fluctuations at a rate of 2 giga entangled bits per second spanning over 4 GHz
bandwidth. The device is operated as a traveling wave parametric amplifier
under Kerr-relieving biasing conditions. Furthermore, we realize the first
successfully demonstration of single-mode squeezing in such devices --
$3.1\pm0.7$\,dB below the zero-point level at half of modulation frequency.
