An arXiv preprint identifies a conditional barrier for a narrow class of security proofs involving QMA witness encryption and null-qIO, a classical-output case of quantum indistinguishability obfuscation. The formal input includes yes-instances paired with quantum witnesses.
The broader question is whether qIO - or even WE for QMA - can be built from standard assumptions. If a QMA–QCIP[2] gap problem exists, the paper says every falsifiable assumption is either false or cannot support the restricted reduction it studies for proving the QMA witness-encryption scheme secure.
The premise is a formal gap assumption that the paper does not concretely instantiate. Basing it on concrete quantum hardness or an oracle separation is left open.
The work appears as arXiv version 1, dated 25 August 2026.
A proof built around two adversaries
The analysis uses formal yes- and no-instance distributions. Yes-instances come with quantum witnesses, while the no-instance distribution may be sampled inefficiently.
The reductions under study preserve the security parameter, use non-adaptive classical queries, and query only honestly generated ciphertexts. That access rule defines the part of the proof landscape covered by the paper.
The proof follows a simulatable-adversary strategy: it pairs a computationally unbounded breaker with an efficient simulator whose behavior is meant to be indistinguishable under the reduction's permitted query access.
One technical step concerns Bayes error, the residual mistake rate of a posterior-based decoder. For every inverse-polynomial threshold γ, the probability that a sampled no-instance has Bayes error at least γ(n) is negligible; the statement concerns the distribution, not every individual no-instance.
A separate hidden-test analysis concludes that an optimal prover decrypts all ciphertexts, supporting the simulator used in the argument.
What the theorems say
For witness encryption, the theorem's conclusion is narrow but strong: under the gap assumption, every falsifiable assumption is either false or cannot support a restricted WE reduction proving the QMA scheme secure.
The qIO conclusion comes through a formal bridge. Assuming null-qIO, the paper says, a WE scheme for QMA exists; that implication is then used to state the corresponding separation for restricted null-qIO reductions.
Under the same gap assumption, the null-qIO theorem says every falsifiable assumption is either false or cannot support a restricted reduction proving the scheme secure.
The proof also constructs a formal adversary with advantage 1/4, while showing that its oracle access can be efficiently simulated.
Where the barrier stops
The boundary is built into the query model. The result covers parameter-preserving reductions with non-adaptive classical queries to honestly generated ciphertexts; broader reduction models are outside the stated result.
On the obfuscation side, the impossibility covers classical-output obfuscators but leaves quantum-state-output obfuscators outside its scope.
The paper deliberately analyzes a WE security notion weaker than the traditional notion.
With the gap premise still uninstantiated, the authors leave open whether it can be based on concrete quantum hardness or an oracle separation. The result therefore marks a boundary around one restricted proof strategy, not an unconditional answer to whether qIO or WE can be built from standard assumptions.
Paper data and sources
Original title: Separating Quantum Indistinguishability Obfuscation from Falsifiable Assumptions
Authors: Mohammed Barhoush, Tomoyuki Morimae, Ramis Movassagh
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text