### Abstract

We study the motion of two non-interacting quantum particles performing a random walk on a line and analyse the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The results are compared to the corresponding classical problem and differences are pointed out. Analytic formulae for the meeting probability and its asymptotic behaviour are derived. The decay of the meeting probability for distinguishable particles is faster than in the classical case, but not quadratically. Entangled initial states and the bosonic or fermionic nature of the walkers are considered.

Original language | English |
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Article number | 009 |

Pages (from-to) | 14965-14983 |

Number of pages | 19 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 48 |

DOIs | |

Publication status | Published - Dec 1 2006 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Štefaňk, M., Kiss, T., Jex, I., & Mohring, B. (2006). The meeting problem in the quantum walk.

*Journal of Physics A: Mathematical and General*,*39*(48), 14965-14983. [009]. https://doi.org/10.1088/0305-4470/39/48/009