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Quantum Information Processing

, Volume 13, Issue 2, pp 559–572 | Cite as

Decoherence in quantum Markov chains

  • Raqueline Azevedo Medeiros SantosEmail author
  • Renato Portugal
  • Marcelo Dutra Fragoso
Article

Abstract

It is known that under some assumptions, the hitting time in quantum Markov chains is quadratically smaller than the hitting time in classical Markov chains. This work extends this result for decoherent quantum Markov chains. The decoherence is introduced using a percolation-like graph model, which allows us to define a decoherent quantum hitting time and to establish a decoherent-intensity range for which the decoherent quantum hitting time is quadratically smaller than the classical hitting time. The detection problem under decoherence is also solved with quadratic speedup in this range.

Keywords

Quantum Markov chains Percolation Decoherence   Quantum hitting time 

Notes

Acknowledgments

We thank F.L. Marquezino for fruitful discussions. The authors acknowledge financial support from FAPERJ n. E-26/100.484/2012, CNPq, and CAPES.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Raqueline Azevedo Medeiros Santos
    • 1
    Email author
  • Renato Portugal
    • 1
  • Marcelo Dutra Fragoso
    • 1
  1. 1.Laboratório Nacional de Computação Científica (LNCC)PetrópolisBrazil

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