Related papers: Optimized quantum f-divergences
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…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched R\'enyi relative…
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states. We establish quantum Hoeffding bounds under a set of structural assumptions, orthogonal to…
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…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We consider a two-parameter family of R\'enyi relative entropies $D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative entropies (or…
This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several…
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…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed…