Related papers: A strengthened data processing inequality for the …
The noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions. For instance, the worst-case ratio of output relative entropy to input relative entropy for all possible pairs of input…
In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum…
The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of…
In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we…
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 paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
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 technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of…
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…
Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality…
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…
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…
We consider a new functional inequality controlling the rate of relative entropy decay for random walks, the interchange process and more general block-type dynamics for permutations. The inequality lies between the classical logarithmic…
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…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels…