Censorship of quantum resources against quantum catalysis

In quantum censorship, an agency oversees quantum communication in a public-domain network. The agency restricts the users' communication to the free states of a quantum resource theory. Despite quantum correlations being fragile, any realistic censorship leaves behind some quantumness, raising concerns that censorship may be overcome through revival or distillation of quantum resources. Here, we introduce censorship protocols that do not require a perfect erasure of a quantum resource, but rather deem censorship successful if users are unable to restore the original quantum state using free operations. We investigate under which conditions censorship is secure, and when it might fail. Moreover, we address the issue of account sharing in quantum networks, wherein independent parties assist in transmitting quantum resources to censored users. This connects resource censorship to timely topics such as quantum catalysis and resource-assisted communication. Censorship protocols offer a novel perspective on quantum network security, that differs fundamentally from existing approaches such as quantum and postquantum cryptography.