Composition of p, and p2 is just P1 0 p2 For pure state p1=|中1)(中1|andp2= 2〉(φ2, the joint state is p1)(φ1∞|φ2)(φ2 =(|1)|φ2)(1∞(2|) Recall tensor product of matrices 1b1a1b12 12011a12b C11012 12 11021110221202101222 21a22 21 22 21b1a21b12a22b11 a21b21a21b22a22b21a22b22• Composition of 𝜌1 and 𝜌2 is just 𝜌1 ⊗ 𝜌2 – For pure state 𝜌1 = 𝜙1 𝜙1 and 𝜌2 = 𝜙2 𝜙2 , the joint state is 𝜙1 𝜙1 ⊗ 𝜙2 𝜙2 = 𝜙1 ⊗ 𝜙2 𝜙1 ⊗ 𝜙2 • Recall tensor product of matrices: 𝑎11 𝑎12 𝑎21 𝑎22 ⊗ 𝑏11 𝑏12 𝑏21 𝑏22 = 𝑎11𝑏11 𝑎11𝑏12 𝑎11𝑏21 𝑎11𝑏22 𝑎12𝑏11 𝑎12𝑏12 𝑎12𝑏21 𝑎12𝑏22 𝑎21𝑏11 𝑎21𝑏12 𝑎21𝑏21 𝑎21𝑏22 𝑎22𝑏11 𝑎22𝑏12 𝑎22𝑏21 𝑎22𝑏22