This work investigates the fundamental limits of implementing network oblivious transfer via noisy multiple access channels and broadcast channels between honest-but-curious parties when the parties have access to general tripartite non-signaling correlations. By modeling the shared resource as an arbitrary tripartite non-signaling box, we obtain a unified perspective on both the channel behavior and the resulting correlations. Our main result demonstrates that perfect oblivious transfer is impossible. In the asymptotic regime, we further show that even negligible leakage cannot be achieved, as repeated use of the resource amplifies the receiver(s)'s ability to distinguish messages that were not intended for him/them. In contrast, the receiver(s)'s own privacy is not subject to a universal impossibility limitation.

翻译：本研究探讨了在诚实但好奇的参与方能够访问一般三方非定域关联的情况下，通过噪声多址信道和广播信道实现网络不经意传输的基本限制。通过将共享资源建模为任意三方非定域关联盒，我们获得了对信道行为和所产生关联的统一视角。我们的主要结果表明，完美的不经意传输是不可能的。在渐近机制下，我们进一步证明即使是可忽略的泄露也无法实现，因为资源的重复使用会放大接收方区分非预期消息的能力。相比之下，接收方自身的隐私并不受普遍不可能性限制的约束。