  Oxide interfaces exhibit a broad range of physical effects stemming from
broken inversion symmetry. In particular, they can display non-reciprocal
phenomena when time reversal symmetry is also broken, e.g., by the application
of a magnetic field. Examples include the direct and inverse Edelstein effects
(DEE, IEE) that allow the interconversion between spin currents and charge
currents. The DEE and IEE have been investigated in interfaces based on the
perovskite SrTiO$_3$ (STO), albeit in separate studies focusing on one or the
other. The demonstration of these effects remains mostly elusive in other oxide
interface systems despite their blossoming in the last decade. Here, we report
the observation of both the DEE and IEE in a new interfacial two-dimensional
electron gas (2DEG) based on the perovskite oxide KTaO$_3$. We generate 2DEGs
by the simple deposition of Al metal onto KTaO$_3$ single crystals,
characterize them by angle-resolved photoemission spectroscopy and
magnetotransport, and demonstrate the DEE through unidirectional
magnetoresistance and the IEE by spin-pumping experiments. We compare the
spin-charge interconversion efficiency with that of STO-based interfaces,
relate it to the 2DEG electronic structure, and give perspectives for the
implementation of KTaO$_3$ 2DEGs into spin-orbitronic devices.
