Tensor products (intro)
General · Mathematics
Study notes
Q: In ℝ²⊗ℝ², express (1,0)⊗(0,1)+(0,1)⊗(1,0). Is it a pure tensor? Basis: e₁⊗e₁, e₁⊗e₂, e₂⊗e₁, e₂⊗e₂. Element: e₁⊗e₂ + e₂⊗e₁. Pure? (ae₁+be₂)⊗(ce₁+de₂) = ace₁⊗e₁+...: need ac = 0, bd = 0, ad = 1, bc = 1. ad = 1, bc = 1: a,d,b,c ≠ 0: ac ≠ 0: contradiction! NOT pure (entangled - Bell state!)!