{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# Examples and features\n", "\n", "In this section we will showcase the different features of Inflation progressively through a series of examples." ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## Compatibility problems\n", "\n", "One of the basic functionalities of Inflation is addressing compatibility problems of probability distributions with causal models. These were illustrated in the [Tutorial](https://ecboghiu.github.io/inflation/_build/html/tutorial.html) section. Here we revisit briefly the examples, and complement them with further functionality, such as extraction of infeasibility certificates and rephrasing feasibility problems in optimization ones.\n", "\n", "### Example 1: Infeasibility of the 2PR distribution in the quantum tripartite line scenario\n", "\n", "Let us begin by recalling the example considered in the [Tutorial](https://ecboghiu.github.io/inflation/_build/html/tutorial.html), namely the compatibility of the 2PR distribution,\n", "\n", "$$ P_{\\text{2PR}}(a,b,c|x,y,z) := \\frac{1+ (-1)^{a+b+c+xy+yz}}{8}, $$\n", "\n", "with the tripartite line scenario, described by the following DAG\n", "\n", "
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