  The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain
non-Hermitian lattice Hamiltonians, particularly those with nonreciprocal
couplings, can host an extensive number of eigenmodes condensed to the
boundary, called skin modes. Although the NHSE has mostly been studied in the
classical regime, we show that it can also manifest in quantum systems
containing boson number nonconserving processes arising from uniform parametric
driving. We study lattices of coupled nonlinear resonators that can function as
reciprocal quantum amplifiers. A one-dimensional chain exhibiting NHSE can
perform strong photon amplification, aided by the skin modes, that scales
exponentially with the chain length and outperforms alternative lattice
configurations that lack the NHSE. We show also that two-dimensional nonlinear
lattices can perform directional photon amplification between different lattice
corners, due to the two-dimensional NHSE.
