An Analysis of the Quantum Penny Flip Game using Geometric Algebra

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...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2009-05, Vol.78 (5), p.54801
Main Authors: CHAPPELL, James M, IQBAL, Azhar, LOHE, M. A, VON SMEKAL, Lorenz
Format: Article
Language:English
Subjects:
Exact sciences and technology
Geometry, differential geometry, and topology
Mathematical methods in physics
Physics
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Summary: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 θ,φ. For comparison we derive the same general winning strategy by conventional means using density matrices.
ISSN:0031-9015
1347-4073
DOI:10.1143/jpsj.78.054801