Reachability Probabilities of Quantum Markov Chains

  • Shenggang Ying
  • Yuan Feng
  • Nengkun Yu
  • Mingsheng Ying
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8052)


This paper studies three kinds of long-term behaviour, namely reachability, repeated reachability and persistence, of quantum Markov chains (qMCs). As a stepping-stone, we introduce the notion of bottom strongly connected component (BSCC) of a qMC and develop an algorithm for finding BSCC decompositions of the state space of a qMC. As the major contribution, several (classical) algorithms for computing the reachability, repeated reachability and persistence probabilities of a qMC are presented, and their complexities are analysed.


quantum Markov chains reachability persistence 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Shenggang Ying
    • 1
    • 2
  • Yuan Feng
    • 1
    • 2
  • Nengkun Yu
    • 1
    • 2
  • Mingsheng Ying
    • 1
    • 2
  1. 1.Tsinghua UniversityChina
  2. 2.University of TechnologySydneyAustralia

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