Censorship of quantum resources against catalytic account sharing

TL;DR

Addresses censorship of quantum resources in public-domain quantum networks. Proposes an operational censorship framework using resource-reducing channels $\Omega$ within quantum resource theories (QRTs) to suppress nonfree resources while leaving free states intact. Develops a multipartite security criterion: censorship is secure if no free-operation can restore the pre-censorship state, and analyzes how account sharing via catalytic transformations can defeat censorship, especially through swapping channels. Studies the coherence resource as a concrete example, showing both secure and breakable regimes, and connects censorship to broader topics such as quantum catalysis and resource embezzlement, offering a security-centric lens distinct from standard cryptography.

Abstract

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 (QRT). 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 post-quantum cryptography.

Figures (2)

• Figure 1: In a resource censorship, an agency oversees quantum communication in a public-domain network by applying a resource-reducing channel $\Omega$ before further transmission of a quantum message. To break the censorship, the senders combine their quantum resources (tangled lines) for improved transmission and the receivers coordinate their classical resources (dashed lines) for state recovery.
• Figure 2: Ordering of multipartite states by free operations. If the state after censorship $\Omega^{\otimes N}(\rho)$ lies in the blue region it is less resourceful than $\rho$, i.e., $\Omega^{\otimes N}(\rho)\nrightarrow \rho$. States in the red region allow for a recovery of $\rho$ using free operations, marking a breakable censorship. In the light gray region lie states which cannot be freely converted into $\rho$, but neither can $\rho$ be freely converted into them. The state after censorship $\Omega^{\otimes N}(\rho)$ cannot lie in these regions, as $\Omega^{\otimes N}$ is itself a free operation.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• Definition 3
• Theorem 1
• Theorem 2
• Proposition 1
• proof
• Theorem 3
• proof
• Theorem 4