Shot noise in an electron waveguide √(NOT) gate

We present a calculation of the shot noise in a ballistic electron waveguide √(NOT) gate. A general expression for the shot noise in the leads connected to these types of gates is shown. We then parametrize an S-matrix which qualitatively describes the action of a √(NOT) gate previously found through numerical methods for GaAs/AlxGa1-xAs based waveguide systems. Using this S-matrix, the shot noise in a single output lead and across two output leads is calculated. We find that the measurement of the shot noise across two output leads allows for the determination of the fidelity of the gate itself