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

In discussing the security of Layer 2 (L2) solutions in relation to quantum threats, it is essential to recognize that these technologies share a security level comparable to their underlying Layer 1 (L1) systems, such as Bitcoin. This parity in security means that any argument suggesting the vulnerability of L2 to quantum threats would concurrently apply to Bitcoin itself, potentially invalidating its utility as well.

Furthermore, while fund security is not the sole attribute of a payment system, it is undeniably crucial. The assertion emphasizes that without robust fund security, a payment system does not fundamentally differ from the legacy financial systems it aims to improve upon. The presence of additional features becomes inconsequential if the basic criterion of fund security is not met, as the primary role of such systems is to offer a secure means of transaction that surpasses traditional financial methods.