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

The discussion revolves around the security and utility of a post-quantum (PQ) Layer 2 (L2) solution in relation to Bitcoin's current Layer 1 (L1) technology, addressing quantum computing threats. The argument presented is that an L2 doesn't inherently introduce new vulnerabilities but inherits its security properties from the L1. This implies that if a quantum computer could compromise the L1 by deriving private keys from public ones, it would similarly affect the L2. However, the primary role of the L2 isn't just to enhance security against quantum threats but to improve the usability of Bitcoin for payments, which aligns with Bitcoin's original purpose.

Furthermore, the correspondent highlights the importance of privacy features that L1 does not offer. In this context, PQ signatures and encryption on the L2 can protect transactions from future quantum attacks, thereby adding a layer of security that doesn't rely on the L1's quantum resistance. Moreover, the design considerations for peg-outs are discussed, emphasizing how these are structured to minimize exposure and risk by limiting the use of classical signatures to critical points only.

Additionally, the readiness of the L2 to adapt to future advancements in Bitcoin's core technology without major overhauls is pointed out. This includes potential upgrades like P2QRH (BIP-360), QuBit, or Lamport signatures in Script, which would allow immediate migration of the peg without compromising user funds, showcasing proactive measures in anticipation of quantum advancements.

In essence, while the current non-PQ nature of Bitcoin's L1 limits the full potential of a PQ L2, the latter still serves as a crucial intermediary step, reducing the amount of sensitive information vulnerable to future quantum decryption. The existence of such initiatives indicates ongoing efforts to address quantum threats proactively rather than reactively, suggesting a strategic approach to blockchain security in the face of evolving technological landscapes.