For α>2, every quantum relative entropy extending the classical Rényi relative entropy is upper bounded by D_{α,α-1}, which is therefore the maximal quantum Rényi relative entropy.
Explicitly,x∼yif and only if there existz 1,...,z n∈Ssuch that x⊴z 1⊵z 2⊴···⊵z n⊴y.(99) We denote the component homomorphisms of∥·∥by∥·∥ (j), forj= 1,...,d
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Maximal R\'enyi Relative Entropy for $\alpha>2$
For α>2, every quantum relative entropy extending the classical Rényi relative entropy is upper bounded by D_{α,α-1}, which is therefore the maximal quantum Rényi relative entropy.