Quantum network exploration with a faulty sense of direction

TL;DR

This paper models exploring quantum networks with a distracted sense of direction, analyzing how adaptive strategies and control resources affect the ability of quantum agents to explore and attain positions.

Contribution

It introduces a new model for quantum network exploration considering distraction and adaptiveness, highlighting the importance of control resources and strategy types.

Findings

Without proper adaptiveness, quantum exploration differs from classical results.

Control resources help maintain the number of attained positions under limited visits.

Adaptive strategies are crucial for effective quantum network exploration.

Abstract

We develop a model which can be used to analyse the scenario of exploring quantum network with a distracted sense of direction. Using this model we analyse the behaviour of quantum mobile agents operating with non-adaptive and adaptive strategies which can be employed in this scenario. We introduce the notion of node visiting suitable for analysing quantum superpositions of states by distinguishing between visiting and attaining a position. We show that without a proper model of adaptiveness, it is not possible for the party representing the distraction in the sense of direction, to obtain the results analogous to the classical case. Moreover, with additional control resources the total number of attained positions is maintained if the number of visited positions is strictly limited.