# Introduction to the quantum first detection problem

We consider quantum dynamics on a graph, with repeated strong measurements performed locally at a fixed time interval τ. For example a particle starting on node *x* and measurements performed on another node *x'*. From the basic postulates of quantum mechanics the string of measurements yields a sequence no,no,no, ... and finally in the *n*-th attempt a yes, i.e. the particle is detected. Statistics of the first detection time *n*τ are investigated, and compared with the corresponding classical first passage problem. Dark states, Zeno physics, a quantum renewal equation, winding number for the first return problem (work of A. Grunbaum et al.), total detection probability, detection time operators and time wave functions are discussed.

**References**

[1] H. Friedman, D. Kessler, and E. Barkai, *Quantum walks: the first detected passage time problem*, **Phys. Rev. E.** **95**, 032141 (2017). *Editor's suggestion.*

[2] F. Thiel, E. Barkai, and D. A. Kessler, *First detected arrival of a quantum walker on an infinite line*, **Phys. Rev. Lett.** **120**, 040502 (2018).

- Last modified: 26/02/2019