  We present a numerically efficient method for the characterisation of a
quantum process subject to dissipation and noise. The master equation evolution
of a maximally entangled state of the quantum system and a non-evolving ancilla
system is simulated by Monte-Carlo wave-functions. We show how each stochastic
state vectors provides quantities that are readily combined into an average
process \chi-matrix. Our method significantly reduces the computational
complexity in comparison with standard characterisation methods. It also
readily provides an upper bound on the trace distance between the ideal and
simulated process based on the evolution of only a single wave function of the
entangled system.
