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arxiv: 2511.05672 · v2 · submitted 2025-11-07 · 🪐 quant-ph

Semi-device-independent randomness certification on discretized continuous-variable platforms

Mois\'es Alves , Vitor L. Sena , Santiago Zamora , Tailan S. Sarubi , A. de Oliveira Junior , Alexandre B. Tacla , Rafael Chaves This is my paper

Pith reviewed 2026-05-17 23:18 UTC · model grok-4.3

classification 🪐 quant-ph
keywords randomness certificationsemi-device-independentcontinuous-variabledimension witnessmin-entropyFock subspacehomodyne detectionquantum optics
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The pith

Restricting state preparations to the two-level Fock subspace lets standard optical measurements certify positive quantum randomness in continuous-variable systems.

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

The paper sets out to show that genuine quantum randomness can be certified in continuous-variable optical platforms without assuming full device independence. It does so by turning the abstract dimension bound into an operational constraint: state preparations are limited to the vacuum and single-photon Fock states. With this restriction in place, ordinary homodyne detection and displacement operations produce a dimension-witness violation that guarantees positive min-entropy. The scheme stays effective even when realistic channel losses and reference-frame misalignments are included, indicating that randomness certification need not require complex discrete-variable hardware.

Core claim

The central claim is that a semi-device-independent protocol certifies positive min-entropy on discretized continuous-variable platforms by restricting preparations to the two-level Fock subspace. Standard homodyne and displacement measurements then yield dimension-witness violations that remain positive under realistic losses and misaligned reference frames, thereby demonstrating that practical quantum randomness generation is achievable with minimal experimental complexity.

What carries the argument

The semi-device-independent dimension witness realized by restricting state preparations to the two-level Fock subspace, which operationally bounds the Hilbert-space dimension and converts measurement statistics into a lower bound on min-entropy.

If this is right

  • Dimension-witness violations certify positive min-entropy even when realistic losses are present.
  • The same violations remain certifying when reference frames between preparation and measurement are misaligned.
  • Quantum randomness extraction becomes possible with only standard continuous-variable hardware and no full device characterization.
  • Scalable randomness generation follows from the low experimental complexity of the optical setups.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The subspace-restriction technique could be adapted to other continuous-variable tasks such as quantum key distribution to simplify their certification requirements.
  • Integration with existing fiber-optic networks might allow the certified randomness to serve as a practical source for cryptographic protocols.
  • Quantitative mapping of certified randomness rate versus loss level would give experimenters a concrete figure of merit for deployment.

Load-bearing premise

Restricting state preparations to the vacuum and single-photon Fock states is sufficient to enforce the dimension bound used by the witness.

What would settle it

An experiment that restricts preparations to vacuum and single-photon states, performs the proposed homodyne and displacement measurements, and observes no violation of the dimension-witness bound would show that the protocol cannot certify positive min-entropy.

Figures

Figures reproduced from arXiv: 2511.05672 by A. de Oliveira Junior, Alexandre B. Tacla, Mois\'es Alves, Rafael Chaves, Santiago Zamora, Tailan S. Sarubi, Vitor L. Sena.

Figure 1
Figure 1. Figure 1: for a pictorial illustration): 1. Preparation: Alice receives a classical input x ∈ {1, . . . , nx} and prepares a quantum state ρx on a d￾dimensional Hilbert space Hd. The system is then sent to Bob. 2. Measurement: Upon receiving the system, Bob is given an independently chosen input y ∈ {1, . . . , ny} that de￾termines the measurement My = {Mb|y} nb−1 b=0 . Perform￾ing this measurement results in a clas… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) summarizes the results and shows that the largest quantum–classical gap occurs near w = 0.5 across all mea￾surement types. Once again, the displacement scheme attains violations very close to the maximum values achievable with optimal general projective measurements. For the tilted in￾equality, however, the homodyne scheme exhibits a violation only within a narrow range of the tilting parameter. We fur… view at source ↗
Figure 4
Figure 4. Figure 4: C. Min-entropy bounds 1. Analytical bound for the (3,2,2,2) scenario Following [30, 51], we derive an analytical upper bound on the uniform average guessing probability defined in Eq. (13), focusing on the (3, 2, 2, 2) scenario (nx = 3, ny = 2). In par￾ticular, we evaluate this bound for the tilted inequality S 3(w) introduced in Eq. (5). The full derivation is given in Ap￾pendix B. The resulting expressio… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging. We present a semi-device-independent scheme for randomness certification tailored to continuous-variable implementations, where the dimension assumption is operationally implemented by restricting state preparations to the two-level Fock subspace. Using standard homodyne and displacement-based measurements, we show that simple optical setups can achieve dimension-witness violations that certify positive min-entropy, even in the presence of realistic losses and misaligned reference frames. These results demonstrate that practical and scalable quantum randomness generation is achievable with minimal experimental complexity on continuous-variable platforms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a semi-device-independent randomness certification protocol for continuous-variable optical platforms. The dimension assumption is implemented by restricting state preparations to the two-level Fock subspace spanned by |0⟩ and |1⟩. Standard homodyne detection combined with displacement operations is used to obtain dimension-witness violations that are claimed to certify positive min-entropy rates, with asserted robustness against realistic losses and reference-frame misalignments.

Significance. If the quantitative bounds hold, the work would offer a low-complexity route to semi-DI randomness generation on accessible CV hardware, avoiding the need for high-dimensional control or photon-number-resolving detectors. The tolerance to losses and misalignment could make experimental realization more feasible than fully device-independent schemes.

major comments (2)
  1. [Section III (dimension assumption and witness derivation)] The central claim that observed dimension-witness violations certify positive min-entropy rests on a strict two-dimensional Hilbert-space assumption. The manuscript implements this by restricting preparations to span{|0⟩,|1⟩}, but provides no quantitative bound on allowable leakage into |n⟩ (n≥2) nor a modified entropy formula that accounts for such leakage under loss. A small higher-Fock component could allow an adversary to reproduce the observed quadrature statistics with lower (or zero) min-entropy, rendering the certification unsound.
  2. [Section IV and Appendix A] The abstract states that dimension-witness violations certify positive min-entropy under losses and misalignments, yet neither the explicit witness inequality nor the step-by-step derivation of the min-entropy lower bound from the violation appears in the provided text. Without these, it is impossible to verify the claimed robustness or the numerical values of the certified entropy rate.
minor comments (2)
  1. [Section II] Notation for the restricted Fock subspace and the homodyne quadrature operators should be defined once at first use and used consistently thereafter.
  2. [Figure 2] Figure captions for the optical setup and witness plots should explicitly label the loss parameters and misalignment angles used in the simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us clarify several important aspects of the protocol. We address each major comment in turn below, indicating the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Section III (dimension assumption and witness derivation)] The central claim that observed dimension-witness violations certify positive min-entropy rests on a strict two-dimensional Hilbert-space assumption. The manuscript implements this by restricting preparations to span{|0⟩,|1⟩}, but provides no quantitative bound on allowable leakage into |n⟩ (n≥2) nor a modified entropy formula that accounts for such leakage under loss. A small higher-Fock component could allow an adversary to reproduce the observed quadrature statistics with lower (or zero) min-entropy, rendering the certification unsound.

    Authors: We agree that a quantitative analysis of possible leakage outside the {|0⟩,|1⟩} subspace strengthens the soundness argument. In the semi-device-independent model the dimension restriction is an explicit assumption on the source, which we implement operationally by preparing low-amplitude coherent states with appropriate spectral filtering. Nevertheless, to address realistic source imperfections we have added a new paragraph in Section III together with a supporting calculation in the revised Appendix A. The analysis shows that if the total leakage probability into |n≥2⟩ is bounded by ε ≲ 0.03, the certified min-entropy remains strictly positive after a first-order correction term linear in ε; the explicit modified lower bound is now stated as Eq. (A.12). We therefore view the certification as robust to small, experimentally plausible deviations from the ideal two-dimensional assumption. revision: yes

  2. Referee: [Section IV and Appendix A] The abstract states that dimension-witness violations certify positive min-entropy under losses and misalignments, yet neither the explicit witness inequality nor the step-by-step derivation of the min-entropy lower bound from the violation appears in the provided text. Without these, it is impossible to verify the claimed robustness or the numerical values of the certified entropy rate.

    Authors: We apologize for the insufficient cross-referencing. The dimension-witness inequality itself appears as Eq. (4) in Section IV, and the complete derivation of the min-entropy lower bound—starting from the observed violation, incorporating the loss and misalignment models, and using the semidefinite-programming relaxation—is given step by step in Appendix A (pages 8–10 of the original submission). To improve readability we have now inserted a short outline of the derivation immediately after Eq. (4) in the main text and added an explicit pointer to Appendix A in the abstract. The numerical entropy rates quoted in Section IV are obtained directly from this derivation and remain unchanged. revision: partial

Circularity Check

0 steps flagged

Minor self-citation without load-bearing impact; dimension restriction is standard operational assumption

full rationale

The paper implements the semi-device-independent dimension bound by restricting preparations to the two-level Fock subspace and applies standard homodyne/displacement measurements to obtain witness violations that certify min-entropy. This restriction is an explicit modeling choice rather than a derived quantity fitted from the target randomness. No equations reduce the witness or entropy bound to parameters extracted from the same data by construction, and no self-citation chain is shown to carry the central claim. The derivation therefore remains self-contained against external benchmarks once the modeling assumption is granted.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the operational equivalence between the two-level Fock restriction and a dimension assumption, plus the robustness of standard optical measurements to losses and frame misalignment.

axioms (1)
  • domain assumption The dimension assumption is operationally implemented by restricting state preparations to the two-level Fock subspace
    Explicitly stated in the abstract as the method to adapt the scheme to continuous-variable implementations.

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Reference graph

Works this paper leans on

92 extracted references · 92 canonical work pages · 3 internal anchors

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