Abstract
A model of joint random walk of two agents in an infinite plane is considered. The agents possess no means of mutual classical communication, but have access to quantum-entanglement resources which are used according to a pre-arranged protocol. The trajectories of the agents diverge on average, but the rate of divergence might be slowed down or speeded up (compared to ordinary random walk) depending on the details of the protocol. This effect has purely quantum nature and can be interpreted in terms of spherical or hyperbolic geometries for slowdown or speedup, respectively.
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