An analysis of the quantum penny flip game using geometric algebra

Copyright © 2009 The Physical Society of JapanWe 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 θ,φ. For comparison we derive the same general winning strategy by conventional means using density matrices. ©2009 The Physical Society of JapanJames M. Chappell, Azhar Iqbal, M. A. Lohe and Lorenz von Smeka