Quantum copy protection, introduced by Aaronson, enables giving out a quantum program-description that cannot be meaningfully duplicated. Despite over a decade of study, copy protection is only known to be possible for a very limited class of programs. As our first contribution, we show how to achieve "best-possible" copy protection for all programs. We do this by introducing quantum state indistinguishability obfuscation (qsiO), a notion of obfuscation for quantum descriptions of classical programs. We show that applying qsiO to a program immediately achieves best-possible copy protection. Our second contribution is to show that, assuming injective one-way functions exist, qsiO is concrete copy protection for a large family of puncturable programs -- significantly expanding the class of copy-protectable programs. A key tool in our proof is a new variant of unclonable encryption (UE) that we call coupled unclonable encryption (cUE). While constructing UE in the standard model remains an important open problem, we are able to build cUE from one-way functions. If we additionally assume the existence of UE, then we can further expand the class of puncturable programs for which qsiO is copy protection. Finally, we construct qsiO relative to an efficient quantum oracle.

翻译：量子复制保护由Aaronson提出，它允许分发无法被有意义地复制的量子程序描述。尽管经过了十多年的研究，但已知的复制保护仅适用于非常有限的程序类别。作为我们的第一个贡献，我们展示了如何为所有程序实现“最佳可能”的复制保护。为此，我们引入了量子态不可区分性混淆（qsiO），这是一种针对经典程序的量子描述的混淆概念。我们证明，将qsiO应用于一个程序可立即实现最佳可能的复制保护。我们的第二个贡献是表明，假设单射单向函数存在，则qsiO为一大类可穿孔程序提供了具体的复制保护——显著扩展了可复制保护的程序类别。我们证明中的一个关键工具是一种新的不可克隆加密（UE）变体，我们称之为耦合不可克隆加密（cUE）。虽然在标准模型中构造UE仍然是一个重要的未解决问题，但我们能够从单向函数构造cUE。如果进一步假设UE存在，则我们可以进一步扩展qsiO作为复制保护的可穿孔程序类别。最后，我们相对于一个高效量子谕言构造了qsiO。