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arxiv: 2606.10436 · v1 · pith:GWTNKPHUnew · submitted 2026-06-09 · 🪐 quant-ph

Analytical performance evaluation of quantum radar architectures: From single-photon to entangled-noise radars

Hossein Allahverdi , Ali Motazedifard This is my paper

Pith reviewed 2026-06-27 13:22 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum radarentangled noise radarsingle-photon radardetection rangeLambert W functionrange enhancement factormicrowave photon detection
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The pith

Analytical expressions using the Lambert W function give the maximum detection range for single-photon and entangled-noise quantum radars.

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

The paper analyzes two classes of quantum radars: single-photon direct-detection systems that use microwave-photon detectors for higher sensitivity, and quantum-entangled noise radars. It derives closed-form expressions for the maximum detection range of each in terms of the Lambert W function after incorporating system parameters, target properties, and environmental factors. The resulting formulas enable direct numerical comparison between noise-based and direct-detection approaches and show that an entangled-noise radar functions as a direct-detection radar equipped with an improved effective threshold signal-to-noise ratio. A range enhancement factor is introduced to measure the performance gain of the entangled quantum version over classical-correlated noise radars, along with a practical approximation rule for that factor.

Core claim

The central claim is that the maximum detection range for both single-photon direct-detection quantum radars and quantum-entangled noise radars can be expressed analytically using the Lambert W function once all relevant system, target, and environmental parameters are included, and that the entangled noise radar can therefore be regarded as an enhanced direct-detection radar possessing an effective threshold signal-to-noise ratio.

What carries the argument

The Lambert W function expressions for maximum detection range that fold in every listed system, target, and environmental parameter, together with the range enhancement factor (REF) that quantifies the advantage of quantum entanglement over classical noise correlation.

If this is right

  • Direct comparison between noise radars and direct-detection radars becomes possible through the shared analytical form.
  • A quantum-entangled noise radar behaves as a direct-detection radar whose effective threshold signal-to-noise ratio is lowered by entanglement.
  • The range enhancement factor quantifies how much farther the entangled version reaches than its classical-correlated counterpart.
  • A simple rule-of-thumb approximation exists for the range enhancement factor.
  • Current microwave detection technology already permits entangled-noise radars with maximum ranges on the order of a few kilometers, with the best results obtained by combining a quantum transducer and an optical-photon detector.

Where Pith is reading between the lines

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

  • - The antenna limitation identified in the analysis implies that further range gains would require targeted improvements in microwave antenna design rather than detector upgrades alone.
  • - The closed-form range expressions could be used to optimize operating frequencies or bandwidths for specific atmospheric conditions not explicitly varied in the paper.
  • - Side-by-side experimental comparison of entangled and classical noise radars under identical parameters would directly test the predicted range enhancement factor.
  • - The few-kilometer feasibility window opens the possibility of testing these radars in short-range remote-sensing or perimeter-monitoring scenarios.

Load-bearing premise

The models for signal propagation, target reflectivity, and noise statistics are assumed to permit a closed-form solution via the Lambert W function without additional approximations that would invalidate the range expressions.

What would settle it

A laboratory or field measurement of actual maximum detection range for a given set of system, target, and environmental parameters that deviates systematically from the numerical value returned by the Lambert W expression.

Figures

Figures reproduced from arXiv: 2606.10436 by Ali Motazedifard, Hossein Allahverdi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: b shows the received photon rate, Rr = Pr/h f , as a function of the transmitted photon rate, Rt = Pt/h f , and the target range R. In this figure, the white-dashed lines indicate the minimum transmitted photon rate that is required to detect the target at given range for each value of SNRth. If the transmitted photon rate falls below the respective threshold curve, the photon rate of the received signal w… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The schematic diagram of a mono-static noise radar [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) (a) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) The normalized Pearson correlation coefficient [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) The effective threshold [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) (a) [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (Color online) (a) Comparison of the physical detection limit of various microwave detection technologies. (b) [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: demonstrates that the considered quantum￾entangled noise radar can detect a stealth aircraft with an RCS around σ ≈ 10−4 m2 at ranges up to 271 m (206 m) in the search (track) mode. A typical stealth aircraft travels at speeds of 200−700 m/s. By considering the minimum warning time required for its detection as 60 seconds, then the necessary detection range is obtained to be 12 − 42 km, which greatly exce… view at source ↗
read the original abstract

This article presents a comprehensive analysis of two classes of quantum radars, including quantum direct-detection and quantum-entangled noise radars. In the first case, inspired by the well-established concept of single-photon LiDARs, we investigated the performance of single-photon radars, in which state-of-the-art single microwave-photon detectors are employed to enhance the detection sensitivity and enable the detection of weaker signals. We derived analytical expressions for the maximum detection range of both classes of quantum radars in terms of the Lambert W function, by considering all relevant system, target, and environmental parameters. Our formulation facilitates direct comparison of noise radars with direct-detection radars and suggests that a quantum-entangled noise radar can be regarded as an enhanced direct-detection radar with an effective threshold signal-to-noise ratio. Furthermore, we applied this framework to classical-correlated noise radars and defined the parameter range enhancement factor (REF) to quantify the superiority of quantum-entangled noise radars over their classical counterparts. Moreover, we introduced a rule-of-thumb for approximating the REF. We also examined the influence of limitations imposed by various microwave detection technologies. Our analysis shows that the conventional antennas limit the potential benefits of quantum-entangled noise radar systems. We also demonstrated that the optimal detection method for these radars is a microwave detector based on a quantum transducer combined with a single optical-photon detector. We showed that, with the current technology, implementing a quantum-entangled noise radar with the maximum detection range on the order of few kilometers is possible. Finally, we explored the potential applications of quantum-entangled noise radars.

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

1 major / 2 minor

Summary. The manuscript analyzes two classes of quantum radars: single-photon direct-detection radars and quantum-entangled noise radars. It derives closed-form analytical expressions for maximum detection range in both cases using the Lambert W function after incorporating system, target, and environmental parameters. The work frames quantum-entangled noise radars as enhanced direct-detection systems with an effective SNR threshold, introduces a range enhancement factor (REF) to quantify gains over classical-correlated noise radars, supplies a rule-of-thumb approximation for the REF, evaluates limitations from current microwave detection technologies, identifies quantum-transducer-plus-optical-photon-detector as optimal, and concludes that few-kilometer ranges are feasible with present technology.

Significance. If the derivations hold exactly, the paper supplies a useful closed-form framework that enables direct, parameter-inclusive comparison of quantum radar architectures without requiring numerical simulation for each scenario. The explicit Lambert W expressions and the REF metric constitute concrete, falsifiable tools for performance evaluation; the identification of technologically feasible detection chains and the practical range estimate are additional strengths that could inform experimental road-mapping in quantum radar research.

major comments (1)
  1. [Derivation of maximum detection range] Derivation of maximum detection range (section presenting the Lambert W expressions): the central claim that the SNR or photon-count threshold equation rearranges exactly into canonical Lambert-W form x exp(x) = g(parameters) must be verified by displaying the intermediate detection-threshold equation and the algebraic rearrangement steps. Any non-exponential factors arising from entangled-noise statistics, transduction efficiency, or atmospheric propagation would invalidate the closed-form claim unless shown to cancel or be negligible.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'all relevant system, target, and environmental parameters' would be clearer if accompanied by an explicit enumeration or reference to the parameter list used in the range formulas.
  2. [REF approximation] REF rule-of-thumb: a short derivation or error-bound analysis for the approximation would strengthen the practical utility claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comment. We address the single major comment below.

read point-by-point responses

  1. Referee: [Derivation of maximum detection range] Derivation of maximum detection range (section presenting the Lambert W expressions): the central claim that the SNR or photon-count threshold equation rearranges exactly into canonical Lambert-W form x exp(x) = g(parameters) must be verified by displaying the intermediate detection-threshold equation and the algebraic rearrangement steps. Any non-exponential factors arising from entangled-noise statistics, transduction efficiency, or atmospheric propagation would invalidate the closed-form claim unless shown to cancel or be negligible.

    Authors: We agree that the intermediate steps must be shown explicitly. In the revised manuscript we will insert the detection-threshold equation (SNR or photon-count form) together with the algebraic manipulations that reduce it to canonical Lambert-W form x exp(x) = g(parameters). Entangled-noise statistics enter solely through an effective SNR threshold; transduction efficiency appears as a constant multiplicative prefactor that is absorbed into g; atmospheric propagation contributes an exponential attenuation that combines with the range-dependent term to preserve the exact x exp(x) structure. The added derivation will display these cancellations step by step. revision: yes

Circularity Check

0 steps flagged

No circularity: Lambert W range expressions are algebraic rearrangements of detection equations

full rationale

The paper sets up detection threshold equations incorporating system, target, and environmental parameters, then solves for maximum range R via the Lambert W function when the functional form permits exact rearrangement to x exp(x) = g(parameters). This is a direct mathematical inversion of the model equations rather than a self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation. No uniqueness theorems, ansatzes, or prior author results are invoked to force the form; the REF is explicitly defined as a comparative metric. The derivation chain is therefore self-contained and externally verifiable against the stated propagation and noise models.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the Lambert W appearance implies an implicit SNR-threshold model whose details are not provided.

pith-pipeline@v0.9.1-grok · 5810 in / 1184 out tokens · 20983 ms · 2026-06-27T13:22:59.967756+00:00 · methodology

discussion (0)

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