Pre-shared Entanglement Sets Quantum Communication Lower Bounds for Private Message Protocols
The preprint establishes bidirectional reductions between QDRE size and QPSM communication complexity. It proves linear lower bounds on quantum messages when entanglement is linear and constant upper bounds for Clifford channels. Pre-shared entanglement is shown to be the central parameter controlling both encoding size and communication cost.
The work maps quantum decomposable randomized encodings to quantum private simultaneous message protocols, proving that constant-output channels admit O(1) quantum communication with exponential entanglement while general channels require linear communication under linear entanglement. Clifford-induced channels achieve O(1) communication with only linear entanglement, separating structured from unstructured cases. These bounds are obtained by reducing channel simulation to communication complexity and constructing explicit protocols that trade entanglement for message size.
The results tighten prior communication-complexity separations and highlight that entanglement is not merely a resource but the decisive parameter separating constant from linear quantum cost. Because the paper remains a 2026 preprint without peer review or independent verification, the concrete cryptographic implications for quantum-secure messaging stay provisional.
Future work could test whether the Ω(n) lower bound survives under noisy entanglement or extends to multi-party settings, directly affecting protocol design for quantum networks.
Huang et al.: A peer-reviewed version or follow-up will appear within 18 months demonstrating whether the linear lower bound holds for all channels under noisy linear entanglement.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2609.17690)
- [2]Supporting Source(https://arxiv.org/abs/2305.12345)