What does "post-quantum" actually mean for a Bitcoin L2 when settlement still happens on a non-PQ L1?

The discussion revolves around the inherent vulnerabilities in layer 1 (L1) systems that are not post-quantum (PQ) secure and their implications for layer 2 (L2) systems, even if those L2 systems employ PQ security measures. It highlights a critical security flaw where, in the absence of PQ security at the L1 level, it becomes possible for an unauthorized entity to derive private keys from public keys. This capability allows them to execute transactions that can effectively transfer control of funds to any L2 system. Consequently, regardless of whether the L2 system incorporates PQ security protocols, the lack of PQ security at the L1 leaves it susceptible to such breaches.

This vulnerability underscores the interconnectedness of security protocols across different layers of blockchain technology. The point made is that securing only the higher layers (like L2) with PQ standards while leaving the foundational layers (like L1) vulnerable does not sufficiently protect against potential quantum-enabled attacks. Such scenarios emphasize the necessity for a holistic approach to implementing PQ cryptography across all layers of blockchain infrastructure to ensure comprehensive security against quantum threats. This approach is vital for maintaining the integrity and trustworthiness of blockchain transactions and safeguarding against the loss of control over digital assets.