6 research outputs found
Investigating Properties of a Family of Quantum Renyi Divergences
Audenaert and Datta recently introduced a two-parameter family of relative
R\'{e}nyi entropies, known as the --relative R\'{e}nyi entropies.
The definition of the --relative R\'{e}nyi entropy unifies all
previously proposed definitions of the quantum R\'{e}nyi divergence of order
under a common framework. Here we will prove that the
--relative R\'{e}nyi entropies are a proper generalization of the
quantum relative entropy by computing the limit of the - divergence
as approaches one and is an arbitrary function of . We
also show that certain operationally relevant families of R\'enyi divergences
are differentiable at . Finally, our analysis reveals that the
derivative at evaluates to half the relative entropy variance, a
quantity that has attained operational significance in second-order quantum
hypothesis testing.Comment: 15 pages, v2: journal versio