F(ρ,σ) = tr[√(√(ρ)σ√(ρ))] = ||√(ρ)√(σ)||_1
of two quantum states ρ and σ can also be expressed as
F(ρ,σ) = tr(√(ρσ)).
Not sure how well-known this is! It is proved in arxiv.org/abs/2211.02623 (or the older arxiv.org/abs/1503.00304).
F(ρ,σ) = tr[√(√(ρ)σ√(ρ))] = ||√(ρ)√(σ)||_1
of two quantum states ρ and σ can also be expressed as
F(ρ,σ) = tr(√(ρσ)).
Not sure how well-known this is! It is proved in arxiv.org/abs/2211.02623 (or the older arxiv.org/abs/1503.00304).