Decoherence in Quantum Markov Chains
  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 the classical hitting time. The detection problem under decoherence is also solved with quadratic speedup in this range. 
Raqueline A. M. Santos, Renato Portugal, Marcelo D. Fragoso
quant-ph