On Removing Interaction from Quantum Proofs

Nicholas Spooner; Max Tromanhauser

Paper 2026/1795

On Removing Interaction from Quantum Proofs

Nicholas Spooner

, Cornell University

Max Tromanhauser

, Cornell University

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) $\Sigma$-protocol for NP using the Fiat–Shamir transformation. Broadbent and Grilo introduced a quantum analog of a $\Sigma$-protocol (which they call a $\Xi$-protocol) in which the prover's first message is quantum, and show that HVZK $\Xi$-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.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Contact author(s): nspooner @ cornell edu
mft55 @ cornell edu
History: 2026-08-26: approved; 2026-08-25: received; See all versions
Short URL: https://ia.cr/2026/1795
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1795,
      author = {Nicholas Spooner and Max Tromanhauser},
      title = {On Removing Interaction from Quantum Proofs},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1795},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1795}
}