A Class Of Maps On Quantum States Preserving Quantum Entropy

Surjective maps on quantum states preserving quantum entropy of convex combinations have been characterized in [4]. In the paper, we generalize this result. Let S(H) be the set of all quantum states on a complex Hilbert space H with dimH=n,2<n<∞and S(p) the quantum entropy of the quantum state p. We show that for arbitrary a surjective map φ:S(H)�'S(H),φ satisfies for arbitrary p,σ∈S(H) and t∈[0,1], there exists∈6[0,1] such that S(tp+(1-t)σ)=S(sφ(ρ)+(1-s)φ(σ)) if and only if there exists a unitary or anti-unitary operator U on H such that φ(ρ)=UpU*for all ρ∈S(H).