An Analysis of the Quantum Penny Flip Game using Geometric Algebra

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.

8 Pages, 1 Figure, accepted for publication in the Journal of Physical Society of Japan

References in corpus (3)

• A necessary and sufficient condition to play games in quantum mechanical settings
• Constructing quantum games from non-factorizable joint probabilities
• Duality, Phase Structures and Dilemmas in Symmetric Quantum Games

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