Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The meeting problem in the quantum random walk   We study the motion of two non-interacting quantum particles performing a
random walk on a line and analyze 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 formulas for the meeting probability and
its asymptotic behavior are derived. The decay of the meeting probability for
distinguishable particles is faster then in the classical case, but not
quadratically faster. Entangled initial states and the bosonic or fermionic
nature of the walkers are considered.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph