Measurement of the statistical state S is given by the map S ↦ ↦ ∑ ∑ λ λ E A ⁡ ⁡ ( λ λ ) S E A ⁡ ⁡ ( λ λ ) . That is, immediately after measurement, the statistical state is a classical distribution over the eigenspaces associated with the possible values λ of the observable: S is a mixed state.