Conditional Quantum Walk and Iterated Quantum Games
arXiv:quant-ph/0607143 · doi:10.1016/j.physa.2008.04.036
Abstract
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
References in corpus (10)
- Quantum random walks - an introductory overview
- A Quantum Random Walk Search Algorithm
- Quantum Games and Quantum Strategies
- Quantum strategies
- Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor
- Quantum Walk on a Line with Two Entangled Particles
- Toward a general theory of quantum games
- Quantum walk on the line: entanglement and non-local initial conditions
- Efficiency and formalism of quantum games
- A Quantum Algorithm for the Hamiltonian NAND Tree
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