Related papers: Doubly minimized Petz and sandwiched Renyi mutual …
We provide a transparent, simple and unified treatment of recent results on the equality conditions for the data processing inequality (DPI) of the sandwiched quantum R\'enyi divergence, including the statement that equality in the data…
Quantum generalizations of R\'enyi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be particularly useful: the Petz quantum R\'enyi…
In [Berta et al., J. Math. Phys. 56, 022205 (2015)], we recently proposed Renyi generalizations of the conditional quantum mutual information of a tripartite state on $ABC$ (with $C$ being the conditioning system), which were shown to…
The conditional quantum mutual information $I(A;B|C)$ of a tripartite state $\rho_{ABC}$ is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is…
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite…
Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy…
We derive a new bound on the effectiveness of the Petz map as a universal recovery channel in approximate quantum error correction using the second sandwiched R\'{e}nyi relative entropy $\tilde{D}_{2}$. For large Hilbert spaces, our bound…
Sandwiched (quantum) $\alpha$-R\'enyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications…
In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…
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…
The optimized quantum $f$-divergences form a family of distinguishability measures that includes the quantum relative entropy and the sandwiched R\'enyi relative quasi-entropy as special cases. In this paper, we establish physically…
The matrix-based Renyi's \alpha-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
Learning disentangled representations of textual data is essential for many natural language tasks such as fair classification, style transfer and sentence generation, among others. The existent dominant approaches in the context of text…
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…
We study the R\'enyi mutual information $\tilde{I}_n$ of the ground state of different critical quantum chains. The R\'enyi mutual information definition that we use is based on the well established concept of the R\'enyi divergence. We…
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…
Quantum information decoupling is a fundamental quantum information processing task, which also serves as a crucial tool in a diversity of topics in quantum physics. In this paper, we characterize the reliability function of catalytic…