Conditional and unconditional information inequalities: an algebraic example

TL;DR

This paper presents an algebraic example demonstrating that certain conditional information inequalities cannot be derived from unconditional ones, highlighting fundamental differences in information inequality structures.

Contribution

The paper introduces a simple algebraic example that illustrates the independence of some conditional information inequalities from unconditional inequalities.

Findings

Conditional inequalities are not derivable from unconditional ones.

Some weak forms of conditional inequalities are fundamentally independent.

The example clarifies the structure of information inequalities.

Abstract

We provide a simple example showing that some conditional information inequalities (even in a weak form) cannot be derived from unconditional inequalities.