  Weak measurement of a subset of noncommuting observables of a quantum system
can be modeled by the open-system evolution, governed by the master equation in
the Lindblad form. The open-system density operator can be represented as
statistical mixture over non unitarily evolving pure states, driven by the
stochastic Nonlinear Schrodinger equation (sNLSE). The globally stable solution
of the sNLSE is obtained in the case where the measured subset of observables
comprises the spectrum-generating algebra of the system. This solution is a
generalized coherent state (GCS), associated with the algebra. The result is
based on proving that GCS minimize the trace-norm of the covariance matrix,
associated with the spectrum-generating algebra.
