Quantum tic-tac-toe: A teaching metaphor for superposition in quantum mechanics

Abstract

Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child’s game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move (“spooky” marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.