Kinetic uncertainty relations for quantum transport

We analyze the precision of currents in a generic multi-terminal quantum-transport setting. Employing scattering theory, we show that the precision of the currents is limited by a function of the particle-current noise that can be interpreted as the activity in the classical limit. We thereby establish a kinetic uncertainty relation for quantum transport. In the full quantum limit, we find precision bounds in which we modify the activity constraints depending on whether the system is fermionic or bosonic. We expect these bounds to be guidelines for any transport process aiming at high precision.