Information theoretic parameters of non-commutative graphs and convex corners

03/25/2021
by   Gareth Boreland, et al.
0

We establish a second anti-blocker theorem for non-commutative convex corners, show that the anti-blocking operation is continuous on bounded sets of convex corners, and define optimisation parameters for a given convex corner that generalise well-known graph theoretic quantities. We define the entropy of a state with respect to a convex corner, characterise its maximum value in terms of a generalised fractional chromatic number and establish entropy splitting results that demonstrate the entropic complementarity between a convex corner and its anti-blocker. We identify two extremal tensor products of convex corners and examine the behaviour of the introduced parameters with respect to tensoring. Specialising to non-commutative graphs, we obtain quantum versions of the fractional chromatic number and the clique covering number, as well as a notion of non-commutative graph entropy of a state, which we show to be continuous with respect to the state and the graph. We define the Witsenhausen rate of a non-commutative graph and compute the values of our parameters in some specific cases.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/24/2023

Fractional eternal domination: securely distributing resources across a network

This paper initiates the study of fractional eternal domination in graph...
research
06/18/2017

Entropy, neutro-entropy and anti-entropy for neutrosophic information

This approach presents a multi-valued representation of the neutrosophic...
research
08/31/2022

Generalizing Körner's graph entropy to graphons

Körner introduced the notion of graph entropy in 1973 as the minimal cod...
research
12/18/2018

On zero-free regions for the anti-ferromagnetic Potts model on bounded-degree graphs

For a graph G=(V,E), k∈N, and a complex number w the partition function ...
research
04/07/2020

A System of Billiard and Its Application to Information-Theoretic Entropy

In this article, we define an information-theoretic entropy based on the...
research
07/21/2022

Noncommutative extensions of parameters in the asymptotic spectrum of graphs

The zero-error capacity of a classical channel is a parameter of its con...
research
04/27/2023

Universal Obstructions of Graph Parameters

We introduce a graph-parametric framework for obtaining obstruction char...

Please sign up or login with your details

Forgot password? Click here to reset