which can be interpreted as the state produced by performing the measurement but not recording which outcome occurred, has a von Neumann entropy larger than that of ρ ρ , except if ρ ρ = ρ ρ ′ . It is however possible for the ρ ρ ′ produced by a generalized measurement, or POVM, to have a lower von Neumann entropy than ρ ρ .