Oracle Separation Between Quantum Commitments and Quantum One-wayness

TL;DR

This paper demonstrates, via an oracle separation, that quantum commitments can exist without the existence of quantum one-way state generators, indicating a fundamental difference in their cryptographic assumptions.

Contribution

It provides the first oracle separation showing quantum commitments do not imply quantum one-way state generators, resolving a key open problem in quantum cryptography.

Findings

Quantum commitments can exist without quantum one-way state generators.

The result rules out black-box constructions from one-way state generators to commitments.

Quantum commitments are likely the weakest cryptographic primitive among known primitives.

Abstract

We show that there exists an oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal assumption for cryptography: the weakest cryptographic assumption implied by all of computational cryptography. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open. Our results rule out any black-box construction, and thus settles this crucial open problem, suggesting that quantum commitments (as well as its equivalency class of EFI pairs, quantum oblivious transfer, and secure quantum multiparty computation) appear to be strictly weakest among all known cryptographic primitives.