## Math Beyond the Horizon

Bell Inequalities and XOR games

Bell inequalities are inequalities that all classical probability distributions satisfy. However, quantum systems can violate these inequalities. We describe this using simple games in which questions and answers are either 0 and 1. In these games, a team of two or more players tries to win a prize from a Wizard, who sets the rules and asks the questions. The players can meet to decide on a strategy, but can communicate only with the Wizard once the game begins. Even though the players can not communicate, they can improve their chance of winning when they share a certain type of quantum state, called entangled.

This talk is intended for high school students. Only very basic probability is used and the elementary quantum principles introduced in the first talk will be reviewed to make this talk self-contained.

### Mary Beth Ruskai

Mary Beth Ruskai is a retired professor from the University of Massachusetts, Lowell who was also affiliated with the Institute for Quantum Computing in Canada.