The meeting problem in the quantum walk

M. Štefaňk, T. Kiss, I. Jex, B. Mohring

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish
Article number009
Pages (from-to)14965-14983
Number of pages19
JournalJournal of Physics A: Mathematical and General
Volume39
Issue number48
DOIs
Publication statusPublished - Dec 1 2006

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Quantum Walk
random walk
Random walk
Asymptotic Behavior
Decay
Motion
Line
decay

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 39, No. 48, 009, 01.12.2006, p. 14965-14983.

Research output: Contribution to journalArticle

Štefaňk, M. ; Kiss, T. ; Jex, I. ; Mohring, B. / The meeting problem in the quantum walk. In: Journal of Physics A: Mathematical and General. 2006 ; Vol. 39, No. 48. pp. 14965-14983.
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