Finite-size general security for relativistic phase shift keying via variable-length quantum key distribution

Carlos Pascual-Garc\'ia

Relativistic phase shift keying achieves general security with finite-size signals beyond 12 dB loss

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-07-01 07:33 UTC pith:SXDKL5WF

load-bearing objection RPSK applies variable-length entropy accumulation and conic optimization to DPSK-style QKD to drop repetition-rate limits and reach concrete finite-size rates at 10^5 signals.

arxiv 2605.06249 v2 pith:SXDKL5WF submitted 2026-05-07 quant-ph

Finite-size general security for relativistic phase shift keying via variable-length quantum key distribution

Carlos Pascual-Garc\'ia This is my paper

classification quant-ph

keywords quantum key distributionrelativistic phase shift keyingfinite-size securitygeneral attacksentropy accumulationRényi leftover hashingconic optimization

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper shows that relativistic phase shift keying can be made secure against general adversaries in the finite-size regime. It does so by using variable-length techniques based on entropy accumulation, Rényi leftover hashing, and conic optimization. These methods avoid the repetition rate limits and expensive statistical analysis that burdened earlier differential phase shift keying proofs. The result is positive secret key rates with 100,000 signals at losses over 12 dB, which supports the idea that this scheme can be implemented experimentally with commercial hardware.

Core claim

By considering relativistic phase shift keying and applying variable-length general security techniques via entropy accumulation, together with methods based on Rényi leftover hashing and conic optimization, the scheme achieves secret key rates with 10^5 signals beyond 12 dB.

What carries the argument

variable-length general security techniques via entropy accumulation, Rényi leftover hashing, and conic optimization applied to relativistic phase shift keying

Load-bearing premise

The variable-length general security techniques via entropy accumulation, Rényi leftover hashing, and conic optimization can be applied to RPSK without inheriting the strong repetition rate constraints and costly statistical estimators of prior DPSK proofs.

What would settle it

A re-computation of the conic optimization for 10^5 signals at 12 dB loss producing a non-positive secret key rate would falsify the reported rates.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Achieves secret key rates with 10^5 signals beyond 12 dB
Overcomes repetition rate constraints from prior DPSK security proofs
Avoids costly statistical estimators used in previous work
Demonstrates experimental implementability of RPSK with affordable technologies

Where Pith is reading between the lines

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

The techniques may extend to other differential phase protocols in quantum key distribution.
Finite-size security without repetition constraints could enable higher throughput in real-world QKD systems.
This provides a pathway to close the theory-practice gap in phase-encoded quantum cryptography.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

RPSK applies variable-length entropy accumulation and conic optimization to DPSK-style QKD to drop repetition-rate limits and reach concrete finite-size rates at 10^5 signals.

read the letter

The paper's main move is to define relativistic phase shift keying as a variant that sidesteps the repetition-rate constraints and heavy statistical estimators in recent DPSK security proofs. It then ports over variable-length techniques—entropy accumulation, Rényi leftover hashing, and conic optimization—to produce general security bounds that work with only 10^5 signals and still clear 12 dB loss.

That combination is what is actually new. The security tools themselves are drawn from existing variable-length QKD literature, but the application to this particular phase-shift scheme and the resulting rate numbers constitute a distinct piece of work. If the derivations hold, the result gives a practical path for commercial hardware that earlier analyses blocked.

The soft spot is the lack of any visible equations or proof sketch in the abstract. Without those, it is impossible to check whether the conic optimization bounds transfer cleanly to the RPSK channel or whether any hidden fitting crept into the finite-size analysis. The stress-test note flags no internal contradiction, but that only means the high-level claim is coherent, not that the math is airtight.

The paper is aimed at researchers who build or analyze practical QKD systems and need finite-size results that do not force unrealistically high repetition rates. A reader already familiar with entropy accumulation and conic methods will see the most value.

It deserves a serious referee. The claim is specific enough and the methods established enough that the details are worth checking in review.

Referee Report

0 major / 3 minor

Summary. The manuscript develops a finite-size general security proof for relativistic phase shift keying (RPSK) as an alternative to differential phase shift keying (DPSK) in quantum key distribution. It applies variable-length techniques based on entropy accumulation, Rényi leftover hashing, and conic optimization to remove repetition-rate constraints and costly statistical estimators from prior DPSK analyses, reporting positive secret key rates with 10^5 signals beyond 12 dB loss as evidence of experimental implementability using commercial technologies.

Significance. If the central application of the variable-length security tools holds without hidden constraints, the result strengthens the case for practical QKD by providing a general (non-i.i.d.) finite-size proof that achieves usable rates at modest block sizes. The explicit removal of repetition-rate limitations and the use of conic optimization for tight bounds are concrete strengths that could support experimental follow-up.

minor comments (3)

[§3] §3 (Security proof outline): the transition from the RPSK channel model to the entropy accumulation theorem application should include an explicit statement of the observed statistics and the choice of test rounds to confirm that the variable-length protocol does not reintroduce repetition-rate assumptions.
[Figure 2] Figure 2 and Table 1: the plotted key rates versus loss for 10^5 signals would benefit from error bars derived from the finite-size statistical fluctuations or from the conic optimization duality gap to allow direct assessment of robustness.
[§4.2] §4.2 (Numerical optimization): clarify whether the conic program is solved with a fixed precision or whether the reported rates include a worst-case duality-gap bound; this affects the claim of 'robust proof of experimental implementability'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on finite-size general security for relativistic phase shift keying and the recommendation of minor revision. The report correctly identifies the key contributions of our variable-length approach using entropy accumulation, Rényi leftover hashing, and conic optimization. Since the provided referee report lists no specific major comments, we have no individual points to address point-by-point at this time.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents an application of established variable-length QKD security techniques (entropy accumulation, Rényi leftover hashing, and conic optimization) to the RPSK protocol in order to relax repetition-rate constraints from prior DPSK analyses. No load-bearing derivation step is shown that reduces a claimed prediction or security bound to a fitted parameter, self-citation chain, or definitional equivalence within the paper itself. The central result is framed as a direct transfer of independent, externally developed methods to a new scheme, rendering the argument self-contained against external benchmarks rather than internally forced.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; full text would be needed to populate the ledger.

pith-pipeline@v0.9.1-grok · 5639 in / 1124 out tokens · 25949 ms · 2026-07-01T07:33:34.454021+00:00 · methodology

0 comments

read the original abstract

Differential phase shift keying constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by considering an alternative scheme, herewith denominated relativistic phase shift keying (RPSK). We leverage variable-length general security techniques via entropy accumulation, together with methods based on R\'enyi leftover hashing and conic optimization. Our approach achieves secret key rates with $10^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of RPSK.

Figures

Figures reproduced from arXiv: 2605.06249 by Carlos Pascual-Garc\'ia.

**Figure 1.** Figure 1: Secret key generation rates for DPSK model under different block sizes view at source ↗

**Figure 2.** Figure 2: Secret key generation rates for DPSK under different dark count rates view at source ↗

**Figure 3.** Figure 3: Secret key generation rates for DPSK under values for the R view at source ↗

**Figure 4.** Figure 4: Secret key generation rates for DPSK under different asymmetry factors view at source ↗

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

2 extracted references

[1]

Bennett and Gilles Brassard

[BB84] Charles H. Bennett and Gilles Brassard. Quantum Cryptography: Public Key Dis- tribution and Coin Tossing. InProceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pages 175–179, Bangalore, India, Decem- ber 1984,

1984
[2]

Imperfect detectors for adversarial tasks with applications to quantum key distribution.Quantum, 10:2044, March

[NTL26] Shlok Nahar, Devashish Tupkary, and Norbert L¨ utkenhaus. Imperfect detectors for adversarial tasks with applications to quantum key distribution.Quantum, 10:2044, March

2044

[1] [1]

Bennett and Gilles Brassard

[BB84] Charles H. Bennett and Gilles Brassard. Quantum Cryptography: Public Key Dis- tribution and Coin Tossing. InProceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pages 175–179, Bangalore, India, Decem- ber 1984,

1984

[2] [2]

Imperfect detectors for adversarial tasks with applications to quantum key distribution.Quantum, 10:2044, March

[NTL26] Shlok Nahar, Devashish Tupkary, and Norbert L¨ utkenhaus. Imperfect detectors for adversarial tasks with applications to quantum key distribution.Quantum, 10:2044, March

2044