Relative entropies play important roles in classical and quantum information theory. In this paper, we discuss the sandwiched Rényi relative entropy for α∈(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 Rényi relative entropy on 𝒯(H)+. Such transformations have the form T↦cUTU∗ for each T∈𝒯(H)+, where c>0 and U is either a unitary or an anti-unitary operator on H. Particularly, all surjective maps preserving sandwiched Rényi 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.

中文翻译：

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密度算子上的夹心 Rényi 相对熵

相对熵在经典和量子信息论中起着重要作用。在本文中，我们讨论了夹层 Rényi 相对熵α∈(0,1)在𝒯(H)+（作用于无限维复希尔伯特空间的正迹类算子锥H) 并刻画所有保留夹层 Rényi 相对熵的满射图𝒯(H)+. 这样的变换形式为吨↦Cü吨ü*对于每个吨∈𝒯(H)+， 在哪里C>0和ü是酉算符或反酉算符H. 特别是，所有保留夹层 Rényi 相对熵的满射图𝒮(H)（所有量子态的集合H) 必须由酉运算符或反酉运算符实现。