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REVIEW 5 major objections 5 minor 2 cited by

Selectively Blind Quantum Computation

T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper establishes that universal blind quantum computing cannot be made cheaper by any server-side local expansion of encrypted resource states, and that hiding one of a known set of computations instead can drastically cut the qubits…

desk verdict The SBQC construction is a real, useful protocol idea, but the impossibility half of the paper is not proven as stated; refocus the paper on the selective-blindness construction and it will be worth serious engagement. read the letter →

arxiv 2504.17612 v1 pith:76PY6U5M submitted 2025-04-24 quant-ph

Abbas Poshtvan , Oleksandra Lapiha , Mina Doosti , Dominik Leichtle , Luka Music , Elham Kashefi This is my paper · ORCID
classification quant-ph
keywords blindquantumcomputingUBQCselectivelycomputationmeasurement-basedremotestateexpandercommunicationcomplexityabstractcryptographyno-gotheorem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish two things about blind quantum computing, where a client with a small quantum device delegates a computation to a powerful server without revealing it. First, it claims that no server-side local quantum operation can take one encrypted resource qubit $|+\theta\rangle$ and expand it into two or more independent resource qubits, so the linear-in-circuit quantum communication of UBQC cannot be reduced this way; the no-go is stated as Proposition 1 and Theorem 1. Second, it claims that if the client only needs to hide which of a known set of computations is performed, communication can drop dramatically: the new SBQC protocols hide the choice by masking measurement-angle and graph differences, and are proven perfectly composable in the Abstract Cryptography framework (Theorem 2). The practical point is a trade-off: reveal more about the computation class and pay far fewer qubits.

What carries the argument

The argument runs on two machines. The no-go side is the 'remote state expander' (RSE): a hypothetical server-side CPTP map that turns one encrypted qubit $|+\theta\rangle$ into two resource qubits with independent hidden angles $\rho_A(\theta_1), \rho_B(\theta_2)$; the impossibility is driven by linearity (an isometry would have to map a two-dimensional input span into a restricted subspace) and, for entangled outputs, by Schmidt decomposition forcing equal subsystem entropies. The constructive side is hiding by difference: the future cone of a target node collects every measurement angle that depends on the target's outcome, and only qubit-masked nodes (those in the cone with non-Clifford default angles) require an extra physical qubit from the client; graph differences are concealed by merging $G_0$ and $G_1$ into a common graph $G_M$ and using bridge-and-break operations so the server cannot tell which edges were deleted.

What would settle it

Find any CPTP map $\Lambda$ with $\Lambda(|+\theta\rangle\langle+\theta|) = \rho_A(\theta_1)\otimes\rho_B(\theta_2)$ satisfying conditions (1)-(3) of Theorem 1 for all $\theta$ in the UBQC angle set; an explicit construction would refute the claimed no-go, and a UBQC protocol built from it that remains blind under an unbounded server would refute Proposition 1 directly.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a matched pair of limits. Proposition 1 states that in any UBQC protocol there is no server-side local operation that maps a resource state $|+\theta\rangle$ to states used on two or more graph nodes while preserving completeness and blindness; Theorem 1 backs this with a no-go for any map whose outputs have independent angle parameters and whose output state reveals nothing about $\theta_1$ and $\theta_2$ when $\theta$ is unknown, proved for isometries, quantum channels, and entangled outputs. Lemma 4 extends the damage: even approximate expanders that produce correlated angles allow differential attacks on the angle one-time pad. On the positive side, the paper defines Selectively Blind Quantum Computing (SBQC), where the client chooses one of a publicly known set of unitaries, and gives protocols that mask only the differences: angle masking via future cones (only nodes with non-Clifford angles need physical qubits) and graph masking via merger graphs with bridge-and-break operations. Theorem 2 states that these protocols perfectly construct the 1-of-2 Delegated Quantum Computation resource, so the protection is composable.

Load-bearing premise

The impossibility result hinges on condition (3) of Theorem 1, which demands that when the input angle $\theta$ is unknown the output state $\rho_{A,B}$ reveals no information about $\theta_1$ and $\theta_2$; this is stronger than UBQC's actual blindness requirement, where the transmitted $|+\theta\rangle$ states themselves leak some information about $\theta$ and security comes from masking the measurement transcript.

Editorial extensions

If this is right

  • UBQC's quantum communication cannot be reduced by any server-side local expansion or recycling of encrypted resource states in the plain, information-theoretic model.
  • Any approximate or correlated resource-state distributor is unusable in UBQC: known functional dependencies among angles open a differential attack on the angle one-time pad.
  • The number of encrypted qubits a client must send for full blindness is superlogarithmic in the size of the computation, so some quantum communication is provably necessary.
  • In SBQC, computations that differ by only a few gates require qubits only for the differing nodes and for non-Clifford nodes in their future cones; Clifford-only differences can be hidden classically.
  • The 1-of-2 SBQC protocol is composably secure: it perfectly constructs the 1-of-2 Delegated Quantum Computation resource, so it can be run alongside other protocols without losing blindness.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The no-go may be narrower than it appears: condition (3) is stricter than the blindness UBQC actually enjoys, so the impossibility result leaves open server-side processes that reduce communication while leaking some information about the resource angles, as long as the computation itself stays hidden.
  • SBQC's cost rule suggests a new circuit-compilation objective: arrange non-Clifford gates so their future cones overlap as little as possible with the client's secret parameters, reducing the number of physical qubits the client must send.
  • A natural test is to instantiate SBQC for a practical family such as parameterized quantum circuits where only weights are secret; the protocol predicts the quantum communication cost should scale with the number of weight-dependent non-Clifford gates rather than circuit width.
  • The paper's merged-graph construction is not yet optimized; an efficient algorithm for optimal merger graphs, at least for brickwork or square lattices, would turn the asymptotic savings into concrete resource estimates.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. This paper studies the communication complexity of blind quantum computing. In the first part, the authors propose an impossibility result (Theorem 1, Proposition 1) claiming that no server-side local quantum operation can map a single |+θ> resource state into two or more states usable as independent UBQC resource states, and therefore that such 'remote state expanders' cannot reduce the quantum communication of UBQC. The argument proceeds through a series of lemmas covering isometries, channels, and entangled outputs, plus a lemma on differential attacks against correlated parameters and a counting lower bound. In the second part, the authors introduce Selectively Blind Quantum Computing (SBQC), a functionality that hides which of a set of known computations is performed, and give protocols (Protocols 4 and 5) that mask angle differences, graph differences, and g-flow differences, with a claimed perfect construction of a 1-of-2 Delegated Quantum Computation resource in the Abstract Cryptography framework (Theorem 2).

Significance. The SBQC framework is a genuinely useful way to think about partial blindness, and the masking techniques (future cones, bridge/break operations, merger graphs) are creative and potentially applicable beyond this paper. The abstract-cryptography security proof, while sketched, is an appropriate goal for composable security. However, the impossibility result, which is one of the two headline contributions, is not established: Theorem 1's condition (3) does not match the blindness notion of UBQC, and the supporting lemmas contain invalid steps. If the no-go were correct, it would be a significant conceptual result; as it stands, the first half of the paper does not meet the standards needed to support Proposition 1. The 'communication-optimal' claim for SBQC also lacks a formal lower-bound statement.

major comments (5)
  1. [Sec. 3, Eq. (8)] Condition (3) of Theorem 1 requires that, when θ is unknown, no information about θ1 and θ2 is accessible from the output state ρA,B. This is substantially stronger than the blindness guarantee of UBQC. In Protocol 1 (Sec. 2.3), the resource states |+θ> are sent to the server, and the server may measure them and learn partial information about θ; blindness holds because the full transcript—states, angles δ = φ' + θ + rπ, and outcomes—is independent of the computation φ. The paper itself notes this leakage and compensates with the random bit r. Consequently, a resource state that leaks or correlates θ1 and θ2 is not automatically ruled out by the requirements of a secure UBQC protocol. Proposition 1, which is the central impossibility claim, is derived from Theorem 1 and therefore does not follow. This is the main gap in the paper's first contribution.
  2. [Sec. 3, Lemma 3] The entropy argument in Lemma 3 is invalid. The proof invokes the Schmidt decomposition S(ρA)=S(ρB) and then claims that, because the left side depends only on θ1 and the right side only on θ2, both must equal a constant s independent of θ1 and θ2. But in the map D, θ1 and θ2 are not independent variables; they are both functions of the single input θ. The equality S(ρA(θ1(θ)))=S(ρB(θ2(θ))) is perfectly consistent with both sides varying with θ (e.g., θ1=θ2=θ). The conclusion that ρA and ρB are constant with respect to their parameters is not justified. Since Lemma 3 is the step that extends the no-go to entangled outputs, Theorem 1 is not proven.
  3. [Sec. 3, Lemma 4] Lemma 4 asserts that a known functional dependency θj = f(θi) enables a differential attack on the one-time-padded angles δi and δj, but it does not construct a distinguisher or quantify the advantage. The claim must account for the fact that ri and rj are fresh, independent, uniform bits unknown to the server; a concrete analysis of the joint distribution of (δi,δj) under the two candidate computations is needed. For some dependencies (e.g., f(θ)=θ and φ differences that are multiples of π), the attack may work, but for others it may not; as written, the lemma is an assertion, not a proof. This matters because the lemma is used to argue that the assumptions of Theorem 1 are minimal for UBQC, i.e., that relaxing condition (3) inevitably breaks blindness.
  4. [Sec. 3, Lemma 2] The proof of Lemma 2 reduces the channel case to Lemma 1 via Stinespring dilation, claiming that the existence of Λ implies an isometry G with G|+θ> = |ψθ1>⊗|ψθ2> where the marginals are ρ(θ1) and ρ(θ2). However, Lemma 1 only rules out isometries with pure product outputs of the specific form |+θ1>⊗|+θ2>. A general purification of two mixed states need not be of this form, so the contradiction is not established. This is a further gap in the proof chain of Theorem 1.
  5. [Abstract and Sec. 4] The abstract and introduction state that the SBQC protocol is 'communication-optimal,' but no theorem or lower bound supporting this optimality is provided. Section 4 gives an explicit construction and analyzes its cost, but there is no matching lower bound showing that any protocol with the same selective-blindness guarantees must send at least as many qubits. The optimality claim should either be proven or removed.
minor comments (5)
  1. [Eq. (15)-(16)] The matrix representation of the isometry D2 uses coefficients cosδ and sinδ for the state |+δ>, which is inconsistent with the definition |+θ> = (|0>+e^{iθ}|1>)/√2 given in Sec. 2.1; the correct coefficients are (1+e^{iδ})/2 and (1-e^{iδ})/2. The conclusion of the lemma is unaffected, but the calculation should be corrected.
  2. [Sec. 3, Lemma 2 and before Lemma 3] The name 'Stinespring' is misspelled as 'Steinspring' in two places; please correct.
  3. [Sec. 1.2] The sentence beginning 'In lemma 1 We also show...' appears to be a formatting or editing artifact; the reference to Lemma 1 is out of place and should be rephrased.
  4. [Sec. 4.4.2, Theorem 2 proof] The proof of Theorem 2 is presented as a sequence of reductions and a simulator description rather than a formal AC proof; in particular, the indistinguishability claims in Reduction 1 rely on the no-communication theorem but do not spell out the distinguisher's interface and the simulator's full transcript. The authors should expand this to a complete proof or clearly mark it as a proof sketch.
  5. [Sec. 3.1, Lemma 5] The generalization of the counting argument to continuous parameter sets is described as 'approximately' valid but not formalized; the discretization argument should be made precise or removed.

Circularity Check

1 steps flagged · score 6.0 of 10

Theorem 1's no-go is built on a self-imposed zero-leakage condition; Proposition 1 does not follow from UBQC blindness, while the SBQC construction is independent.

  1. self definitional [Section 3, Theorem 1 (Eq. 8), and its use in Proposition 1]
    "(3) If the parameter θ is unknown, then no information about θ1 and θ2 is accessible from the output ρA,B."

    This condition is not UBQC blindness. Section 2.3 states that measuring a qubit |+θ> 'can leak partial information about the secret key θ' and that security is restored by the one-time-padded angle δ=φ'+θ+rπ and the hidden outcome b=s⊕r. Blindness only requires the server's full transcript to be independent of the computation {φ_i}, not that the transmitted resource states leak no information about θ1 and θ2. By building 'no information about θ1 and θ2' into the definition of the remote state expander, Theorem 1 assumes the very independence that Proposition 1 later presents as a necessary condition for blindness. The impossibility is therefore largely contained in the task definition rather than derived from the security definition of UBQC.

full rationale

The constructive part of the paper, SBQC (Protocols 4 and 5 and Theorem 2), is not circular: the Abstract Cryptography proof proceeds by explicit reductions (EPR-pair preparation, delayed measurement, simulator construction) and does not rely on the no-go theorem. The circularity is concentrated in the impossibility claim. Theorem 1 postulates that a useful remote state expander must satisfy condition (3), i.e. that θ1 and θ2 are inaccessible from the output state. But the paper itself acknowledges in Section 2.3 that standard UBQC resource states |+θ> can leak partial information about θ and that blindness is preserved by the random rπ masking of measurement outcomes and angles. Thus condition (3) is a stronger, self-imposed requirement, not the blindness condition of UBQC. Lemma 4, which is supposed to close the gap by showing dependent parameters break blindness, only asserts that a one-time pad with correlated keys is insecure and never constructs a distinguisher against the UBQC transcript; this is a correctness gap rather than a derivation. Consequently, Proposition 1 does not follow from the stated theorems, and the no-go result is substantially circular: the impossibility is encoded in the condition assumed at the start. The SBQC protocol, by contrast, has independent content and a self-contained security proof, so the paper is only partially circular.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The protocol has no fitted numerical parameters. The main unstated assumption is condition (3) in Theorem 1, which is not the standard UBQC security condition and makes the no-go close to tautological. The SBQC protocol relies on standard MBQC results and the bridge/break operations from [22].

assumptions (5)
  • ad hoc to paper A resource state useful for UBQC must have independent secret parameters θ1, θ2 with no information accessible from the output state alone (Theorem 1 condition (3)).
    This assumption is load-bearing for the impossibility result, but it is stronger than UBQC's actual security notion, where resource states can carry information about θ as long as the measurement transcript is masked. This mismatch undermines Proposition 1.
  • standard math Linearity of quantum mechanics, Stinespring dilation, Schmidt decomposition, and the no-communication theorem.
    Standard background used in Lemmas 1-3 and in the AC security proof of Theorem 2.
  • domain assumption The g-flow condition of Browne et al. is necessary and sufficient for deterministic MBQC computation.
    Used to define future cones and correction rules in Section 4, specifically in Definition 6 and the angle-hiding analysis.
  • domain assumption The server knows the set of candidate unitaries {U0,U1} and the leakage lU0,U1; blindness only requires hiding which unitary is chosen.
    This defines the SBQC security model in Figure 3 and Resource 1, and is the standard selective-blindness setting the paper adopts.
  • domain assumption Bridge and break operations from [22] correctly transform the resource graph as described in Protocols 2 and 3.
    The graph masking technique relies on these known operations; the paper cites [22] rather than re-deriving them.

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Cite this review

Pith. "Pith review of Selectively Blind Quantum Computation." pith.science (2026). https://pith.science/paper/76PY6U5M

@misc{pith2026250417612,
  author       = {Pith},
  title        = {Pith review of: Selectively Blind Quantum Computation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/76PY6U5M}},
  note         = {Machine review of arXiv:2504.17612}
}
read the original abstract

Known protocols for secure delegation of quantum computations from a client to a server in an information theoretic setting require quantum communication. In this work, we investigate methods to reduce communication overhead. First, we establish an impossibility result by proving that server-side local processes cannot decrease quantum communication requirements of secure delegation protocols. We develop no-go results that prohibit such processes within an information theoretic framework. Second, we present a possibility result by introducing Selectively Blind Quantum Computing (SBQC), a novel functionality that allows the client to hide one among a known set of possible computations. We characterize how differences between computations in the protected set influence the number of qubits sent during our SBQC implementation, yielding a communication-optimal protocol. This approach reduces qubit communication drastically and demonstrates the trade-off between information leaked to the server and communication cost.

Figures

Figures reproduced from arXiv: 2504.17612 by the authors.

Figure 1
Figure 1. In green we show all the nodes for which the measurement angle has [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. The ideal functionality of UBQC, in the language of Abstract Cryptog [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. The ideal functionality of Selectively Blind Quantum Computation. Note, that the selection of unitaries {Ui}i=1,...,n is fixed as a public parameter of the func￾tionality, which is available to all participating parties. An honestly participating server does not have access to its interfaces, and its input b is filtered to be 0. 4.1 Angle Masking Techniques In this section we describe how to hide a difference in a d… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The future cone of the red node is shown in green and blue. The green [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: Bridge and break states before and after the protocol. [PITH_FULL_IMAGE:figures/full_fig_p027_5.png]
Figure 6
Figure 6. Figure 6: Teleporting the output values. Red vertices (including dotted red) belong [PITH_FULL_IMAGE:figures/full_fig_p031_6.png]
Figure 7
Figure 7. Figure 7: 1-of-2 DQC Resource. On the Client’s interface, the Resource receives the [PITH_FULL_IMAGE:figures/full_fig_p036_7.png]

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Forward citations

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.