  We present a universal technique for quantum state estimation based on the
maximum-likelihood method. This approach provides a positive definite estimate
for the density matrix from a sequence of measurements performed on identically
prepared copies of the system. The method is versatile and can be applied to
multimode radiation fields as well as to spin systems. The incorporation of
physical constraints, which is natural in the maximum-likelihood strategy,
leads to a substantial reduction of statistical errors. Numerical
implementation of the method is based on a particular form of the Gauss
decomposition for positive definite Hermitian matrices.
