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

The globally stable solution of a stochastic Nonlinear Schrodinger Equation