On Removing Interaction from Quantum Proofs
quant-ph, cs.CR
Submitted: 2026-09-29
Updated: 2026-09-29
License: http://creativecommons.org/licenses/by/4.0/
The gist: An important open question in quantum cryptography is the construction of publicly-verifiable NIZKs for QMA.
Terminology
Abstract
An important open question in quantum cryptography is the construction of publicly-verifiable NIZKs for QMA. Classically, one can construct NIZKs for NP in the random oracle model (and sometimes in the standard model) by compiling an honest-verifier ZK (HVZK) Σ-protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a Σ-protocol (which they call a Ξ-protocol) in which the prover's first message is quantum, and show that HVZK Ξ-protocols exist for QMA. However, it is not clear how to compile such protocols into NIZKs in the (Q)ROM, because the Fiat-Shamir transformation seems to be incompatible with quantum messages. In this work we give formal evidence that this is indeed the case: we show that if generic "Fiat-Shamir-like" compilers for quantum protocols exist in the QROM (with small completeness and soundness error) then QMA = BQP.
Sources
- Quantum Lazy Sampling and Path Recording for Any Group
- Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms
- New security notions and feasibility results for authentication of quantum data
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