The meeting problem in the quantum random walk

Abstract

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.

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• Two-walker discrete-time quantum walks on the line with percolation
• Maximal entanglement from quantum random walks
• Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle
• Quantum Walk with Jumps
• Dynamic conditioning of two particle discrete-time quantum walks
• On the equivalence between quantum and random walks on finite graphs
• Two-particle coined-quantum walk with long-range interaction
• M-Particle Quantum Walks with Delta-Interaction
• Quantum walk on a square lattice with identical particles
• Crossing paths in 2D Random Walks