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Recent advances have lead towards first prototypes of a quantum internet inwhich entanglement is distributed by sources producing bipartite entangledstates with high fidelities. This raises the question which states can begenerated in quantum networks based on bipartite sources using local operationsand classical communication. In this work we study state transformations underfinite rounds of local operations and classical communication in networks basedon maximally entangled two-qubit states. We first derive the symmetries forarbitrary network structures as these determine which transformations arepossible. Then we show that contrary to tree graphs for which it has alreadybeen shown that any state within the same entanglement class can be reachedthere exist states which can be reached probabilistically but notdeterministically if the network contains a cycle. Furthermore, we provide asystematic way to determine states which are not reachable in networksconsisting of a cycle. Moreover, we provide a complete characterization of thestates which can be reached in a cycle network with a protocol where each partymeasures only once and each step of the protocol results in a deterministictransformation. Finally, we present an example which cannot be reached withsuch a simple protocol.

Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication