  We study how unique features of non-Hermitian lattice systems can be
harnessed to improve Hamiltonian parameter estimation in a fully quantum
setting. While the so-called non-Hermitian skin effect does not provide any
distinct advantage, alternate effects yield dramatic enhancements. We show that
certain asymmetric non-Hermitian tight-binding models with a $\mathbb{Z}_2$
symmetry yield a pronounced sensing advantage: the quantum Fisher information
per photon increases exponentially with system size. We find that these
advantages persist in regimes where non-Markovian and non-perturbative effects
become important. Our setup is directly compatible with a variety of quantum
optical and superconducting circuit platforms, and already yields strong
enhancements with as few as three lattice sites.
