Quantum walks: The mean first detected transition time

@article{Liu2020QuantumWT,
  title={Quantum walks: The mean first detected transition time},
  author={Q. Liu and R. Yin and K Ziegler and Eli Barkai},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk in a finite-dimensional Hilbert space where the initial state $|\psi_{\rm in}\rangle$ of the walker is orthogonal to the detected state $|\psi_{\rm d}\rangle$. We focus on diverging mean transition times, where the total detection probability exhibits a… Expand
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