Mixed state A mixed state is a statistical ensemble of pure state. criterion: Pure state: Tr ⁡ ( ρ 2 ) = 1 {\displaystyle \operatorname {Tr} (\rho ^{2})=1} Mixed state: Tr ⁡ ( ρ 2 ) < 1 {\displaystyle \operatorname {Tr} (\rho ^{2})<1}