Classical Commitments to Quantum States

Abstract

We define the notion of a classical commitment to quantum state scheme, which allows a quantum prover to compute a classical commitment to a quantum state and later open each qubit of the state in either the standard or Hadamard basis, while limiting communication with the verifier to a classical channel. Our scheme strengthens the notion of a measurement protocol from [Mah18], which is binding only in the standard basis. We construct our commitment scheme from the post-quantum Learning With Errors (LWE) assumption, and rely directly on any noisy trapdoor claw-free function family that satisfies the adaptive hardcore bit property first introduced in [Bra+18].