Oracle Separations Between Quantum and Non-interactive Zero-Knowledge Classes
Pith reviewed 2026-05-25 01:18 UTC · model grok-4.3
The pith
There exists an oracle A such that NIPZK^A is not contained in BQP^A.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
There exists an oracle A such that NIPZK^A is not a subset of BQP^A. The construction is obtained by a direct extension of a prior oracle that already separated SZK from BQP, using only the definitions and closure properties of NIPZK.
What carries the argument
Direct lift of the prior oracle construction to NIPZK via its closure properties under the relevant reductions and simulations.
If this is right
- The separation between BQP and zero-knowledge classes holds even for the most restrictive non-interactive perfect variant.
- No additional relativized assumptions are needed beyond those already used for SZK.
- Any future collapse of NIPZK into BQP would have to be non-relativizing.
Where Pith is reading between the lines
- The same lifting technique may apply to other restricted proof classes that share similar closure properties.
- Explicit or non-relativizing separations between these classes would require different methods.
- The result constrains possible quantum algorithms for problems that admit non-interactive perfect zero-knowledge proofs.
Load-bearing premise
The definitions and closure properties of NIPZK let the existing oracle construction transfer without introducing new relativized collapses.
What would settle it
An explicit description of the oracle together with a verification that the language placed outside BQP remains in NIPZK relative to that oracle.
read the original abstract
We study the relationship between problems solvable by quantum algorithms in polynomial time and those for which zero-knowledge proofs exist. In prior work, Aaronson [arxiv:quant-ph/0111102] showed an oracle separation between BQP and SZK, i.e. an oracle $A$ such that $\mathrm{SZK}^A \not\subseteq \mathrm{BQP}^A$. In this paper we give a simple extension of Aaronson's result to non-interactive zero-knowledge proofs with perfect security. This class, NIPZK, is the most restrictive zero-knowledge class. We show that even for this class we can construct an $A$ with $\mathrm{NIPZK}^A \not\subseteq \mathrm{BQP}^A$.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript extends Aaronson's oracle separation between BQP and SZK to show that there exists an oracle A such that NIPZK^A is not contained in BQP^A. The argument is presented as a simple extension of the prior SZK construction to the non-interactive perfect zero-knowledge setting.
Significance. If correct, the result would establish that the relativized separation between quantum polynomial-time computation and zero-knowledge holds even for the most restrictive ZK class (non-interactive with perfect security), providing a stronger form of the oracle separation.
major comments (1)
- [Abstract (main claim)] The central claim that Aaronson's oracle A directly witnesses NIPZK^A ⊈ BQP^A rests on the unverified assumption that the NIPZK simulator's indistinguishability and perfect completeness transfer without introducing new relativized failure modes or altering the distinguishing power of A. No explicit argument, modified simulator construction, or verification of statistical distance bounds under the NIPZK definition is supplied.
minor comments (1)
- The reference to Aaronson's prior work (arXiv:quant-ph/0111102) should be expanded to a full bibliographic entry.
Simulated Author's Rebuttal
We thank the referee for the detailed reading and for highlighting the need for explicit verification in the presentation of our extension. We address the concern below and will revise the manuscript accordingly.
read point-by-point responses
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Referee: [Abstract (main claim)] The central claim that Aaronson's oracle A directly witnesses NIPZK^A ⊈ BQP^A rests on the unverified assumption that the NIPZK simulator's indistinguishability and perfect completeness transfer without introducing new relativized failure modes or altering the distinguishing power of A. No explicit argument, modified simulator construction, or verification of statistical distance bounds under the NIPZK definition is supplied.
Authors: We agree that the manuscript would be strengthened by an explicit argument confirming that the simulator properties carry over. The extension is direct because the oracle A is identical to Aaronson's and the NIPZK simulator is a special case of the SZK simulator used in the original construction; perfect completeness holds by the same promise-gap properties, and the statistical distance bound between the simulator output and the real interaction remains unchanged under relativization since no new queries or oracles are introduced. Nevertheless, to eliminate any ambiguity about relativized failure modes, the revised version will add a short subsection (approximately one paragraph) that restates the NIPZK definition, recalls the simulator from Aaronson's SZK protocol, and verifies the statistical-distance and completeness bounds explicitly for the non-interactive perfect case. revision: yes
Circularity Check
No circularity; constructive extension of external oracle result
full rationale
The paper presents an oracle separation NIPZK^A notsubseteq BQP^A by claiming a simple extension of Aaronson's independent 2002 SZK separation. The abstract and description cite an external construction (arXiv:quant-ph/0111102) and rely on standard NIPZK definitions and relativization without any self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. No equations or steps reduce the claimed result to its own inputs by construction; the result is self-contained against the external benchmark oracle.
discussion (0)
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