Now for describing a measurement by an instrument I , the maps E x are used to model the mapping from an input state ρ ρ to the output state of a measurement conditioned on a classical measurement outcome x . Therefore, the probability that a specific measurement outcome x occurs on a state ρ ρ is given by p ( x | ρ ρ ) = tr ⁡ ⁡ ( E x ( ρ ρ ) ) .