  The scattering of quantum particles by non-hermitian (generally nonlocal)
potentials in one dimension may result in asymmetric transmission and/or
reflection from left and right incidence. Eight generalized symmetries based on
the discrete Klein's four-group (formed by parity, time reversal, their
product, and unity) are used together with generalized unitarity relations to
determine the possible and/or forbidden scattering asymmetries. Six basic
device types are identified when the scattering coefficients (squared moduli of
scattering amplitudes) adopt zero/one values, and transmission and/or
reflection are asymmetric. They can pictorially be described as a one-way
mirror, a one-way barrier (a Maxwell pressure demon), one-way (transmission or
reflection) filters, a mirror with unidirectional transmission, and a
transparent, one-way reflector. We design potentials for these devices and also
demonstrate that the behavior of the scattering coefficients can be extended to
a broad range of incident momenta.
