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 nτ 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).