Related papers: Entropy Power Inequality in Fermionic Quantum Comp…
The relative entropy of certain states on the algebra of canonical anticommutation relations (CAR) is studied in the present work. The CAR algebra is used to describe fermionic degrees of freedom in quantum mechanics and quantum field…
Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for…
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…
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…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…
In this study, the quantum R\'{e}nyi entropy power inequality of order $p>1$ and power $\kappa$ is introduced as a quantum analog of the classical R\'{e}nyi-$p$ entropy power inequality. To derive this inequality, we first exploit the…
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: $$f(\sqrt{a}\,X + \sqrt{1-a}\,Y) \ge a f(X) + (1-a) f(Y) \quad \forall…
The canonical anticommutation relations (CAR) for fermion systems can be represented by finite-dimensional matrix algebra, but it is impossible for canonical commutation relations (CCR) for bosons. After description of more simple case with…
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…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the…
Relativistic fermionic field theories constitute the fundamental description of all observable matter. The simplest of the models provide a useful, classically verifiable benchmark for noisy intermediate scale quantum computers. We…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
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…
We examine the weakly interacting atoms in an ultracold Fermi gas leading to a state of macroscopic coherence, from a theoretical perspective. It has been shown that this state can be described as a fermionic coherent state. These coherent…
We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi…
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…
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic…
Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable…