### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*39*(48), 14965-14983. [009]. https://doi.org/10.1088/0305-4470/39/48/009

**The meeting problem in the quantum walk.** / Štefaňk, M.; Kiss, T.; Jex, I.; Mohring, B.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 39, no. 48, 009, pp. 14965-14983. https://doi.org/10.1088/0305-4470/39/48/009

}

TY - JOUR

T1 - The meeting problem in the quantum walk

AU - Štefaňk, M.

AU - Kiss, T.

AU - Jex, I.

AU - Mohring, B.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33947256903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947256903&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/48/009

DO - 10.1088/0305-4470/39/48/009

M3 - Article

AN - SCOPUS:33947256903

VL - 39

SP - 14965

EP - 14983

JO - Journal Physics D: Applied Physics

JF - Journal Physics D: Applied Physics

SN - 0022-3727

IS - 48

M1 - 009

ER -