Quantum correlations in collective strategies of mutual search/anti-search for three parties

Models of joint random walk strategies for three parties on an infinite plane have been considered. They do not have access to communication, external landmarks, and any information about their mutual position, but can use the resource of three-particle quantum spin entanglement distributed between them within the framework of a pre-agreed protocol. Although the trajectories of the parties diverge on average, the rate of this divergence can be increased or decreased by choosing the details of the protocol.