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Quantum walks: Decoherence and coin-flipping games

Author

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  • Romanelli, Alejandro
  • Hernández, Guzmán

Abstract

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.

Suggested Citation

  • Romanelli, Alejandro & Hernández, Guzmán, 2011. "Quantum walks: Decoherence and coin-flipping games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1209-1220.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:6:p:1209-1220
    DOI: 10.1016/j.physa.2010.12.006
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    Cited by:

    1. Stijn De Backer & Luis E. C. Rocha & Jan Ryckebusch & Koen Schoors, 2024. "On the potential of quantum walks for modeling financial return distributions," Papers 2403.19502, arXiv.org, revised Dec 2024.

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