  Magnetars in quiescent states continue to emit hard X-rays with a power far
exceeding the loss of rotational energy. It has recently been noted that this
hard X-ray continuum may bear a direct signature of quantum electrodynamic
(QED) effects in magnetic fields stronger than the Schwinger field ($B_{\rm Q}
= 4.4\times 10^{13}$ G). When the current flowing into the magnetosphere is
driven by narrow structures in the solid crust, the $e^\pm$ pair plasma
supporting the current relaxes to a collisional and trans-relativistic state.
The decay of a pair into two photons produces a broad, bremsstrahlung-like
spectrum of hard X-rays, similar to that observed and extending up to $0.5-1$
MeV. The conversion of two gamma rays to a pair is further enhanced by a factor
$\sim B/B_{\rm Q}$. Monte Carlo calculations of pair creation in a dipole
magnetic field are presented. Non-local particle injection is found to be
strong enough to suppress the high voltage that otherwise would accompany polar
magnetic twist; the hard X-rays are mostly emitted away from the magnetic
poles. Some of the pairs annihilate in an optically thin surface layer. The
prototypical anomalous X-ray pulsar 1E 2259$+$586, which shows a hard X-ray
continuum but relatively weak torque noise, slow spindown, and no radio
emission, is a Rosetta Stone for understanding the magnetar circuit, consistent
with the picture advanced here. For a $15-60$ keV luminosity as low as
$10^{34}$ erg s$^{-1}$, the polar flux of sub-relativistic pairs produces an
optical depth $3-30$ to electron cyclotron scattering in the $1-10$ keV band,
reducing the net X-ray polarization.
