An Analysis of the Quantum Penny Flip Game using Geometric Algebra

TL;DR

This paper uses geometric algebra to analyze the quantum penny flip game, identifying all winning strategies for player Q and providing a clear visual and mathematical derivation of these strategies.

Contribution

It introduces a geometric algebra approach to analyze quantum game strategies, offering a visual and simplified derivation of the winning transformations.

Findings

Identifies all unitary transformations enabling a winning strategy for Q.

Provides a geometric algebra framework for visualizing quantum game strategies.

Derives the winning strategy parametrized by two angles, matching conventional methods.

Abstract

We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum game and its strategies, as well as providing a simple and direct derivation of the winning transformation, which we demonstrate can be parametrized by two angles. For comparison we derive the same general winning strategy by conventional means using density matrices.