Given the diverse array of physical systems available for quantum computing and the absence of a well-defined quantum internet protocol stack, the design and optimisation of quantum networking protocols remain largely unexplored. To address this, we introduce an approach that facilitates the establishment of paths capable of delivering end-to-end fidelity above a specified threshold, without requiring detailed knowledge of the quantum network properties, which we call the 'grey box approach'. In this study, we define algorithms that are specific instances of this approach and evaluate them in comparison to Dijkstra shortest path algorithm and a fully knowledge-aware algorithm through simulations. Our results demonstrate that one of the grey box algorithms consistently outperforms the other methods in delivering paths above the fidelity threshold, across various network topologies and the number of source-destination pairs involved, while maintaining significant levels of fairness among the users and being robust to inaccurate estimations of the expected end-to-end fidelity.

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