Related papers: alpha-z-relative Renyi entropies
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
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 set out to demonstrate that the R\'enyi entropies with parameter $\alpha$ are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the R\'enyi's postulates lead to Pap's g-calculus…
For $\alpha,z>0$ with $\alpha\ne1$, motivated by comparison between different kinds of R\'enyi divergences in quantum information, we consider log-majorization between the matrix functions \begin{align*}…
We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki's variational expression of the relative entropy to an arbitary standard $f$-divergence, from…
The aim of this work is to establish that two recently published projection theorems, one dealing with a parametric generalization of relative entropy and another dealing with R\'{e}nyi divergence, are equivalent under a correspondence on…
Since their introduction in the early sixties, the R\'enyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between…
Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…
We offer the first operational interpretation of the $\alpha$-z relative entropies, a measure of distinguishability between two quantum states introduced by Jak\v{s}i\'c et al. and Audenaert and Datta. We show that these relative entropies…
In this paper, we generalize the log-Sobolev inequalities to R\'enyi--Sobolev inequalities by replacing the entropy with the two-parameter entropy, which is a generalized version of entropy and closely related to R\'enyi divergences. We…
We consider optimal scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long…
Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties…
The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately…
The analogues of Arimoto's definition of conditional R\'enyi entropy and R\'enyi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to…
This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative…
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…
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 coherence is a crucial resource for quantum information processing. By employing the language of coherence orders largely applied in NMR systems, quantum coherence has been currently addressed in terms of multiple quantum coherences…