A new definition of hitting time and an embedded Markov chain in continuous-time quantum walks

We present a new probabilistic definition for the hitting time of a continuous-time quantum walk into a marked set of nodes, when measurements with respect to the canonical basis are performed according to the jump times of a Poisson process. Furthermore, we derive a formula for the calculation of the mean hitting time, based on our novel definition of hitting time, Wald’s theorem and the stochastic process that models our quantum measurement outcomes. This stochastic process results in a Markov chain, whose transition matrix contains the expected values of the squared norm of the entries of a random unitary matrix, and it can be thought as a way to embed a Markov chain in a continuous-time quantum walk.