How to Use Quantum Indistinguishability Obfuscation

Quantum copy protection, introduced by Aaronson [Aar09], enables giving out a quantum programdescription 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 copyprotectable 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.