arxiv: 2604.20573 · v1 · submitted 2026-04-22 · 🪐 quant-ph

Recognition: unknown

Device-independent quantum cryptography with input leakage

V\'ictor Zapatero , Marcos Curty

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Pith reviewed 2026-05-09 23:50 UTC · model grok-4.3

classification 🪐 quant-ph

keywords device-independent quantum cryptographyCHSH inequalityinput leakagerandomness certificationquantum key distributionnoisy channel model

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The pith

Device-independent protocols can certify local randomness and extract secret keys even with partial input leakage by modeling it as an independent noisy channel.

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

The paper relaxes the strict no-leakage assumption in device-independent quantum cryptography by allowing partial leakage of the measurement inputs. It models this leakage as a noisy channel whose effect can be quantified separately from the observed quantum correlations via the CHSH inequality. This yields explicit expressions for the amount of certifiable local randomness and the achievable secret key rate, both of which decrease with increasing leakage magnitude but remain positive up to certain thresholds. A sympathetic reader would care because real devices cannot guarantee perfect input isolation, so these bounds show how much security survives realistic imperfections. The analysis applies to both randomness certification and quantum key distribution tasks.

Core claim

In CHSH-based device-independent randomness certification and key distribution, when input leakage is modeled as an independent noisy channel, the certifiable local randomness and the secret key rate can both be expressed as explicit decreasing functions of the leakage magnitude, remaining strictly positive below well-defined thresholds determined by the observed CHSH violation.

What carries the argument

Modeling input leakage as a noisy channel independent of the quantum correlations, allowing its magnitude to be quantified separately from the CHSH violation to bound randomness and key rates.

Load-bearing premise

The input leakage can be faithfully modeled as a noisy channel whose effect is independent of the quantum correlations and can be quantified separately from the CHSH violation.

What would settle it

An experiment that controls the magnitude of input leakage in a CHSH test, measures the observed violation and leakage level, and checks whether the certified randomness or key rate matches the predicted functional dependence on leakage.

Figures

Figures reproduced from arXiv: 2604.20573 by Marcos Curty, V\'ictor Zapatero.

**Figure 2.** Figure 2: Local guessing probability of Eve in a CHSH [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Lower bound on the asymptotic secret key [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

Device-independence is the gold standard of quantum cryptography. To meet this standard, a central assumption is that no information leakage occurs during protocol execution. We relax this assumption by analyzing CHSH-based randomness certification and key distribution with partial leakage of the inputs, modeled in terms of a noisy channel. Our results quantify the certifiable local randomness and the secret key rate as a function of the magnitude of the input leakage.

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.

Desk Editor's Note private letter to a colleague

This paper gives explicit functions for how much CHSH-based DI randomness and key rate survive when inputs leak through a classical noisy channel.

read the letter

The core result is a set of bounds showing how certified local randomness and secret key rate degrade as a function of input leakage strength in CHSH device-independent protocols. They model the leakage as a fixed noisy classical channel acting on the inputs and derive the surviving quantities directly from that parameter. This is the first place I have seen the dependence written out explicitly rather than left as a qualitative remark about imperfect isolation. It is useful because it turns a realistic implementation problem into something you can measure and plug into the security analysis. The approach stays within the standard DI framework by keeping the leakage external and separate from the quantum correlations, which lets them reuse CHSH violation data with an adjusted input distribution. That modeling choice is reasonable and keeps the analysis tractable. The soft spot is exactly the separation they rely on: the channel must be independent of the devices' internal state and the measurement choices. If an adversary can correlate the leakage with hidden variables or make the effective noise depend on which input is chosen, the extracted bounds no longer apply. The paper treats the leakage magnitude as a known external parameter, so any real deployment would still need an independent way to bound or measure that magnitude. The derivations look like straightforward adjustments to the usual CHSH analysis, but without seeing the full error terms or numerical checks it is hard to judge how tight the bounds end up. This work is aimed at people already doing device-independent randomness or key distribution who need to account for imperfect input isolation. A reader who wants concrete tolerance numbers for a specific leakage level will find it directly usable. It deserves peer review because the question is practical and the modeling is coherent, even if the independence assumption will need careful justification in the full text.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes CHSH-based device-independent randomness certification and quantum key distribution, relaxing the no-leakage assumption by modeling partial input leakage as a classical noisy channel whose effect is independent of the underlying quantum correlations. It derives explicit expressions for the certifiable local randomness and the achievable secret key rate as functions of the leakage magnitude parameter.

Significance. If the modeling separation holds, the work provides concrete, usable bounds that quantify the degradation in DI security guarantees due to realistic input leakage. This is relevant for bridging theoretical DI protocols with experimental implementations where perfect input isolation cannot be guaranteed, and the functional dependence on leakage magnitude allows direct assessment of protocol viability.

major comments (2)

[§2 (Leakage model)] §2 (Leakage model): The central modeling choice treats the input leakage as a noisy channel whose statistics are independent of the quantum state and the specific measurement outcomes, allowing separate quantification from the observed CHSH violation. This independence is load-bearing for all subsequent bounds; an adversary able to correlate the effective channel with hidden variables or the quantum system would invalidate the separation, and the manuscript does not provide a rigorous argument or worst-case bound against such correlation.
[§4 (Randomness and key-rate derivations)] §4 (Randomness and key-rate derivations): The expressions for certifiable local randomness and secret key rate are given as functions of the leakage magnitude, but the derivations rely on the channel independence without an accompanying error analysis or sensitivity check showing how small violations of independence affect the final quantities. This makes it difficult to assess robustness of the claimed quantifications.

minor comments (2)

[Abstract] The abstract and introduction would benefit from a short explicit statement of the CHSH inequality and the standard no-leakage assumption being relaxed.
Notation for the leakage magnitude parameter is introduced without a dedicated table or summary of its allowed range (0 to 1); adding this would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the two major comments point by point below, indicating the changes made in the revised version.

read point-by-point responses

Referee: §2 (Leakage model): The central modeling choice treats the input leakage as a noisy channel whose statistics are independent of the quantum state and the specific measurement outcomes, allowing separate quantification from the observed CHSH violation. This independence is load-bearing for all subsequent bounds; an adversary able to correlate the effective channel with hidden variables or the quantum system would invalidate the separation, and the manuscript does not provide a rigorous argument or worst-case bound against such correlation.

Authors: We thank the referee for this observation. The independence of the leakage channel from the quantum state and measurement outcomes is an explicit modeling assumption introduced in Section 2 to permit a clean separation between classical input leakage and the device-independent quantum correlations. This choice allows us to derive closed-form expressions for the certified quantities as functions of the leakage parameter. We agree that an adversary capable of introducing correlations between the leakage channel and the hidden variables (or the quantum system) would require a different, more complex analysis that could alter the bounds. The manuscript does not claim to cover this stronger adversarial setting. In the revised manuscript we have expanded the discussion in Section 2 to state the modeling assumption more explicitly, to delineate its scope, and to identify correlated leakage as an open direction for future investigation. revision: partial
Referee: §4 (Randomness and key-rate derivations): The expressions for certifiable local randomness and secret key rate are given as functions of the leakage magnitude, but the derivations rely on the channel independence without an accompanying error analysis or sensitivity check showing how small violations of independence affect the final quantities. This makes it difficult to assess robustness of the claimed quantifications.

Authors: The expressions derived in Section 4 are exact under the independence assumption stated in the model. We acknowledge that an explicit sensitivity analysis would help readers gauge robustness against small departures from independence. In the revised manuscript we have added a short subsection in Section 4 that provides a first-order robustness argument: using the continuity of the relevant conditional von Neumann entropies with respect to the channel parameters, we show that the certified local randomness and secret-key rate change continuously when the independence assumption is mildly violated. This addition supplies a quantitative indication of sensitivity without altering the main closed-form results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation treats leakage magnitude as external input parameter

full rationale

The paper derives certifiable local randomness and secret key rate explicitly as functions of an externally quantified leakage magnitude under a modeled noisy channel. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract and reader's summary. The central results are expressed in terms of the leakage parameter rather than reducing to it by construction, and the modeling assumption (channel independence) is stated separately from the CHSH-based quantification. This is a standard self-contained functional derivation against external benchmarks, consistent with score 0-2.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard CHSH Bell inequality plus the new modeling assumption that input leakage acts as an independent noisy channel.

free parameters (1)

leakage magnitude
The parameter that quantifies the strength of the noisy channel; results are expressed as functions of this external parameter.

axioms (2)

standard math CHSH inequality provides the basis for device-independent certification of randomness and keys.
Standard assumption in device-independent quantum information.
domain assumption Input leakage can be modeled as a noisy channel whose statistics are independent of the quantum state and measurement outcomes.
Core modeling choice introduced to relax the no-leakage assumption.

pith-pipeline@v0.9.0 · 5346 in / 1242 out tokens · 37388 ms · 2026-05-09T23:50:33.020249+00:00 · methodology

discussion (0)

Reference graph

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