  We derive the quantum trajectory or stochastic (conditional) master equation
for a single superconducting Cooper-pair box (SCB) charge qubit measured by a
single-electron transistor (SET) detector. This stochastic master equation
describes the random evolution of the measured SCB qubit density matrix which
both conditions and is conditioned on a particular realization of the measured
electron tunneling events through the SET junctions. Hence it can be regarded
as a Monte Carlo method that allows us to simulate the continuous quantum
measurement process. We show that the master equation for the "partially"
reduced density matrix [Y. Makhlin et.al., Phys. Rev. Lett. 85, 4578 (2000)]
can be obtained when a "partial" average is taken on the stochastic master
equation over the fine grained measurement records of the tunneling events in
the SET. Finally, we present some Monte Carlo simulation results for the
SCB/SET measurement process. We also analyze the probability distribution
P(m,t) of finding m electrons that have tunneled into the drain of the SET in
time t to demonstrate the connection between the quantum trajectory approach
and the "partially" reduced density matrix approach.
