Given a density matrix ρ ρ 123 on H , we define a density matrix ρ ρ 12 on H 1 ⊗ ⊗ H 2 as a partial trace : ρ ρ 12 = T r H 3 ρ ρ 123 . Similarly, we can define density matrices: ρ ρ 23 , ρ ρ 13 , ρ ρ 1 , ρ ρ 2 , ρ ρ 3 .