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arxiv: 2604.06457 · v1 · submitted 2026-04-07 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Higher rates for semi-device-independent randomness expansion by recycling input randomness

Rutvij Bhavsar , Hamid Tebyanian , Roger Colbeck
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:44 UTC · model grok-4.3

classification 🪐 quant-ph
keywords semi-device-independentrandomness expansionprepare-and-measurequantum random number generationinput recyclingquantum side informationphotodiode testing
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The pith

Recycling input randomness enables semi-device-independent expansion at high rates after 10^5 to 10^6 rounds

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

The paper introduces two protocols for randomness expansion in a prepare-and-measure setting where the source and measurement devices are uncharacterized. Trust is placed only in a testing device such as a photodiode. One protocol recycles the randomness used to choose inputs, allowing expansion in a small number of rounds while remaining secure against quantum side information. The other uses a biased input distribution when recycling is not feasible. Both achieve high output rates under conditions close to current experiments.

Core claim

In a semi-device-independent prepare-and-measure scenario, recycling the input randomness used to select measurement settings yields randomness expansion at high rates after only 10^5 to 10^6 rounds, with security proven against quantum side information while trusting solely the testing device.

What carries the argument

The input-randomness recycling step inside the semi-device-independent prepare-and-measure protocol, which reuses the same random bits to reduce the net consumption while preserving the security bound.

If this is right

  • Randomness expansion becomes practical with far fewer experimental rounds than previous semi-device-independent schemes.
  • Quantum random number generators can operate while trusting only a simple detector such as a photodiode.
  • The same security guarantee holds when the source and measurement devices are manufactured by an untrusted party.
  • Biased-input variants extend the method to settings where input recycling cannot be applied.

Where Pith is reading between the lines

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

  • Recycling techniques developed here may reduce the round count required in other semi-device-independent tasks such as quantum key distribution.
  • Realistic noise models from current photonic experiments could be inserted into the security analysis to obtain tighter rate estimates.
  • The protocol could be combined with existing trusted-device QRNG hardware to lower overall trust requirements without redesigning the source or detectors.

Load-bearing premise

The testing device can be trusted and fully characterized while the source that prepares states and the measurement device remain completely uncharacterized.

What would settle it

An experiment in which the observed output randomness fails to exceed the input randomness by the predicted margin, or in which an adversary with access to the untrusted devices can guess the output with probability higher than the security analysis allows, would falsify the claimed expansion.

Figures

Figures reproduced from arXiv: 2604.06457 by Hamid Tebyanian, Roger Colbeck, Rutvij Bhavsar.

Figure 1
Figure 1. Figure 1: Schematic illustration of our protocols. The setup consists of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Lower bounds on the function GpX (ω, Θ) for different values of pX. Panel (a) corresponds to the uniform input distribution relevant for Protocol 1, while panel (b) pertains to the heavily biased input distribution associated with Protocol 2. The shaded gray region represents parameter regimes where no quantum strategies achieving the corresponding ω and Θ values exist. The red lines indicate ω = (3 − 2Θ)/… view at source ↗
Figure 3
Figure 3. Figure 3: Asymptotic rates for the protocols as a function of the score [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Finite-size randomness expansion rates for Protocol [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: This figure illustrates the setup starting with a laser in the preparation stage where OOK or amplitude modulation [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A diagram of the measurement round channel [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
read the original abstract

Although quantum random number generators rely on the inherent indeterminism of quantum mechanics, ensuring that the numbers produced are secure remains a significant challenge. We introduce two semi-device-independent randomness expansion protocols in a prepare-and-measure setting, where the source and measurement devices are treated as uncharacterised and we assume trust only in testing device, which could be implemented using a photodiode. One protocol achieves expansion by recycling the input randomness, while the other uses a biased input distribution to achieve expansion in settings where recycling is not possible. The protocols are proven secure against quantum side information. Our results show that high randomness rates are achievable under experimentally realistic conditions, with expansion obtained in as few as $10^5$ to $10^6$ rounds with the recycling protocol.

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

0 major / 3 minor

Summary. The manuscript introduces two semi-device-independent randomness expansion protocols in the prepare-and-measure setting. The source and measurement devices are uncharacterized, with trust placed solely in a testing device (e.g., a photodiode). One protocol achieves expansion by recycling input randomness; the other employs a biased input distribution. Both protocols are proven secure against quantum side information, with numerical results indicating that positive expansion rates are achievable in as few as 10^5 to 10^6 rounds under realistic experimental conditions.

Significance. If the security analysis and finite-size bounds hold, the work advances practical semi-device-independent quantum random number generation by demonstrating higher rates via input recycling and biased inputs. This reduces the experimental overhead compared to prior SDI protocols while maintaining security against quantum adversaries, with the trust model limited to the testing device offering a realistic implementation path.

minor comments (3)
  1. [Abstract] Abstract: the statement that expansion is obtained 'in as few as 10^5 to 10^6 rounds' would benefit from a parenthetical reference to the specific parameters (e.g., observed violation level, noise model, or block size) that yield this threshold, to allow immediate assessment of the numerical claim.
  2. [Security Analysis] The security proof section should explicitly state the form of the min-entropy bound used for the recycled-input case and how the finite-size correction terms are computed (e.g., via Chernoff or Hoeffding bounds), as this is central to verifying the reported rates.
  3. [Numerical Results] Figure captions for the rate-vs-rounds plots should include the exact values of the input bias parameter and the testing-device efficiency assumed in the optimization.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the contributions, and recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces two prepare-and-measure protocols for semi-device-independent randomness expansion, with security proven against quantum side information. The central claims of achievable rates in 10^5-10^6 rounds follow from independent security analysis and numerical bounds rather than any self-definitional reduction, fitted inputs renamed as predictions, or load-bearing self-citations. No step reduces by construction to its own inputs via the paper's equations or prior author work; the derivation remains self-contained against external quantum information benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits extraction; relies on standard quantum mechanics for security and the semi-device-independent trust model. No explicit free parameters or invented entities mentioned.

axioms (2)
  • standard math Quantum mechanics holds and provides the basis for randomness and security proofs
    Invoked implicitly for all quantum randomness and side-information security claims.
  • domain assumption Only the testing device is trusted while source and measurement devices are uncharacterized
    Core semi-device-independent assumption stated in the abstract.

pith-pipeline@v0.9.0 · 5424 in / 1207 out tokens · 34266 ms · 2026-05-10T18:44:11.966403+00:00 · methodology

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Reference graph

Works this paper leans on

61 extracted references · 7 canonical work pages

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    Randomly chooseX i ∈ {0,1}, which is input to the source deviceS. HereXi = 0occurs with probability p0. The deviceSsends a system to the switchW

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    (a) IfT i = 0(measurement round):Mreceives the system and outputsY i ∈ {0,1}. (b) IfT i = 1(test round):Wreceives the system and outputsY i ∈ {0,1}

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