Density matrix If a system is in stateψ1〉 with probability"1, and in state 1 2) with probability p2, then the system is in a mixed state The mixed state is represented as a density matrix p=p1|y)y1|+p21yb2)(y2 In general, if a system is in state l i> with probability pi, then the mixed state is p=∑p21vz For pure state ) p=lyb blDensity matrix • If a system is in state 𝜓1 with probability 𝑝1, and in state 𝜓2 with probability 𝑝2, then the system is in a mixed state. • The mixed state is represented as a density matrix 𝜌 = 𝑝1 𝜓1 𝜓1 + 𝑝2 𝜓2 𝜓2 . • In general, if a system is in state 𝜓𝑖 with probability 𝑝𝑖 , then the mixed state is 𝜌 = σ𝑖 𝑝𝑖 𝜓𝑖 𝜓𝑖 • For pure state 𝜓 , 𝜌 = 𝜓 𝜓