相关论文: The strong converse exponent of discriminating inf…

The sandwiched R\'enyi $\alpha$-divergences of two finite-dimensional quantum states play a distinguished role among the many quantum versions of R\'enyi divergences as the tight quantifiers of the trade-off between the two error…

We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…

In a certain sense we generalize the recently introduced and extensively studied notion called quantum R\'enyi divergence (in another name, sandwiched R\'enyi relative entropy) and describe the structures of corresponding symmetries. More…

We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…

One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured…

We determine the exact strong converse exponent for entanglement-assisted classical communication of a quantum channel. Our main contribution is the derivation of an upper bound for the strong converse exponent which is characterized by the…

There are different inequivalent ways to define the R\'enyi capacity of a channel for a fixed input distribution $P$. In a 1995 paper Csisz\'ar has shown that for classical discrete memoryless channels there is a distinguished such quantity…

We introduce a new quantum R\'enyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an…

In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding…

We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy to normal positive functionals on arbitrary von Neumann algebras, for the values $\alpha>1$. For this, we use Kosaki's definition of noncommutative $L_p$-spaces…

This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…

We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution,…

We study an extension of the sandwiched R\'enyi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $\alpha\in [1/2,1)$. This work is intended as a continuation of [A. Jen\v{c}ov\'a, Ann. Henri…

We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…

We determine the exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity. Our form of the exponent is an exact analogue of Arimoto's, given as a transform of the Renyi capacities with…

Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for $f$-divergences. Universal upper and lower bounds have been provided along with several applications,…

This work presents an infinite-dimensional generalization of the correspondence between the Kullback-Leibler and R\'enyi divergences between Gaussian measures on Euclidean space and the Alpha Log-Determinant divergences between symmetric,…

Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…

This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…

The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…