. The square roots are well defined as both and represent quantum states, being positive semidefinite. For pure quantum states and , we get that .
Properties
- Unitary Group invariance: for all Unitary Operators .
- Symmetry: .
- .
Search
F(ρ,σ):=Tr[ρσρ]2 . The square roots are well defined as both ρ and σ represent quantum states, being positive semidefinite. For pure quantum states ρ=∣ρ⟩⟨ρ∣ and σ=∣σ⟩⟨σ∣, we get that F(ρ,σ)=∣⟨ρ∣σ⟩∣2.