Conditional Quantum Walk and Iterated Quantum Games
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Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary operations. Several frequently used classical strategies give rise to families of corresponding quantum strategies. A quantum version of the Prisoner's Dilemma in which both players use mixed strategies is presented as a specific example. Since there are now quantum walk physical implementations at a proof-of principle stage, this connection may represent a step towards the experimental realization of quantum games.
Revtex 4, 6 pages, 3 figures. Expanded version with one more figure and updated references. Abstract was rewritten
Revtex 4, 6 pages, 3 figures. Expanded version with one more figure and updated references. Abstract was rewritten