Sandwiched Renyi relative entropy on density operators

Relative entropies play important roles in classical and quantum information theory. In this paper, we discuss the sandwiched Renyi relative entropy for alpha is an element of(0, 1) on T(H)(+) (the cone of positive trace-class operators acting on an infinite-dimensional complex Hilbert space H) and characterize all surjective maps preserving the sandwiched Renyi relative entropy on T(H)(+). Such transformations have the form T bar right arrow cUTU* for each T is an element of T(H)(+), where c > 0 and U is either a unitary or an anti-unitary operator on H. Particularly, all surjective maps preserving sandwiched Renyi relative entropy on S(H) (the set of all quantum states on H) are necessarily implemented by either a unitary or an anti-unitary operator.