Abstract
The property of superadditivity of the quantum relative entropy states that, in a bipartite system H_AB=H_A ⊗ H_B, for every density operator ρ_AB one has D( ρ_AB || σ_A ⊗ σ_B ) ≥ D( ρ_A || σ_A ) +D( ρ_B || σ_B) . In this work, we provide an extension of this inequality for arbitrary density operators σ_AB . More specifically, we prove that α (σ_AB)· D(ρ_AB||σ_AB) ≥ D(ρ_A||σ_A)+D(ρ_B||σ_B) holds for all bipartite states ρ_AB and σ_AB, where α(σ_AB)= 1+2 || σ_A^-1/2 ⊗ σ_B^-1/2 σ_AB σ_A^-1/2 ⊗ σ_B^-1/2 - 1_AB ||_∞.