  We demonstrate that an all-antiferromagnetic tunnel junction with current
perpendicular to the plane geometry can be used as an efficient spintronics
device with potential high frequency operation. By using state-of-the-art
density functional theory combined with quantum transport, we show that the
N\'eel vector of the electrodes can be manipulated by spin-transfer torque.
This is staggered over the two different magnetic sublattices and can generate
dynamics and switching. At the same time the different magnetization states of
the junction can be read by standard tunnelling magnetoresistance. Calculations
are performed for CuMnAs$|$GaP$|$CuMnAs junctions with different surface
terminations between the anti-ferromagnetic CuMnAs electrodes and the
insulating GaP spacer. In particular we find that the torque remains staggered
regardless of the termination, while the magnetoresistance depends on the
microscopic details of the interface.
