Related papers: The entropy power inequality for quantum systems
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
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…
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement…
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
Entropic force has been drawing the attention of theoretical physicists following E. Verlinde's work in 2011 to derive Newton's second law and Einstein's field equations of general relativity. In this paper, we extend the idea of entropic…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We compare the entropy-energy inequality and the von Neumann entropic inequality for three level atom implemented on superconducting circuits with Josephson junction. The positivity of entropy and energy relations for the qutrit system are…
The $\alpha$-$z$ R\'enyi relative entropies are a two-parameter family of R\'enyi relative entropies that are quantum generalizations of the classical $\alpha$-R\'enyi relative entropies. In \cite{zhang20CFL} we decided the full range of…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…
Using a sharp version of the reverse Young inequality, and a R\'enyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive R\'enyi entropy power inequalities for log-concave random vectors when…
This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the R\'{e}nyi entropy of a random vector in terms of the two…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…