M Štefanák et al 2006 J. Phys. A: Math. Gen. 39 14965 doi:10.1088/0305-4470/39/48/009
The meeting problem in the quantum walk
M Štefanák1, T Kiss2, I Jex1 and B Mohring3
Show affiliationsWe 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.
- PACS
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05.40.Fb Random walks and Levy flights
- MSC
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82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 48 (1 December 2006)
Received 12 July 2006, in final form 6 September 2006
Published 15 November 2006
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The meeting problem in the quantum walk
M Štefanák et al 2006 J. Phys. A: Math. Gen. 39 14965
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