Related papers: Entropy power inequalities for qudits
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…
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…
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds with the differential entropy replaced by…
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…
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the…
This paper first focuses on deriving an alternative approach for proving an extremal entropy inequality (EEI), originally presented in [11]. The proposed approach does not rely on the channel enhancement technique, and has the advantage…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental…
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…
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
We study quantum computation relations on unital finite-dimensional CAR $C^{*}$-algebras. We prove an entropy power inequality (EPI) in a fermionic setting, which presumably will permit understanding the capacities in fermionic linear…
Quantum Fano inequality (QFI) in quantum information theory provides an upper bound to the entropy exchange by a function of the entanglement fidelity. We give various Fano-like upper bounds to the entropy exchange and QFI is a special case…
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…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
We provide a condition under which a version of Shannon's Entropy Power Inequality will hold for dependent variables. We provide information inequalities extending those found in the independent case.
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…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…