Existing protocols for quantum communication networks usually assume an initial allocation of quantum entanglement resources, which are then manipulated through local operations and classical communication to establish high-fidelity entanglement between distant parties. It is generally held that the resulting fidelity would increase monotonically with the entanglement budget. Here, we show that for noncooperative protocols, the resulting fidelity may decrease as more entanglement is added to a network with nonpure states. This effect results from a quantum analog of selfish routing and constitutes a potential obstacle to the optimal use of resources in large quantum networks.

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• Network flow optimization
• Quantum communication
• Quantum networks
• Quantum protocols
• Resource theories