  We study non-equilibrium differential conductance and current fluctuations in
a single quantum point contact. The two-terminal electrical transport
properties -- differential conductance and shot noise -- are measured at 1.5 K
as a function of the drain-source voltage and the Schottky split-gate voltage.
In differential conductance measurements, conductance plateaus appear at
integer multiples of $2e^2/h$ when the drain-source voltage is small, and the
plateaus evolve to a fractional of $2e^2/h$ as the drain-source voltage
increases. Our shot noise measurements correspondingly show that the shot noise
signal is highly suppressed at both the integer and the non-integer conductance
plateaus. This main feature can be understood by the induced electrostatic
potential model within a single electron picture. In addition, we observe the
0.7 structure in the differential conductance and the suppressed shot noise
around 0.7 ($2e^2/h$); however, the previous single-electron model cannot
explain the 0.7 structure and the noise suppression, suggesting that this
characteristic relates to the electron-electron interactions.
