# ⚛  L1 Principle — Quantum Illumination — entanglement-enhanced target detection

**ID:** `L1-154` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Quantum Imaging — *Two-mode squeezing for target detection below shot-noise*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** binary detection map
> **📡 Carrier:** photon · **🌫 Noise:** shot poisson
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554241

---

## 🧠 1. Introduction

**Quantum Illumination — entanglement-enhanced target detection** is a **nonlinear inverse problem** whose unknown lives in **binary detection map** space, within the **Two-mode squeezing for target detection below shot-noise** sub-domain of **Quantum Imaging**.

Measurements consist of photons collected by an optical detector via a **entanglement detection** sensing mechanism.

The forward operator applies, in order: L · entangled photon source operator; L · signal probe return operator; L · joint detection operator; detector accumulates flux over the exposure window.

Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered binary detection map is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 35); loss_and_noise_decoherence dominates the stability cliff; phase_drift and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.

## ⚙ 2. Forward Model

Physical chain: **x** → L · entangled photon source → L · signal probe return → L · joint detection → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.joint_detection` `L.signal_probe_return` `L.entangled_photon_source` x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.entangled_photon_source` | L · entangled photon source operator |
| `L.signal_probe_return` | L · signal probe return operator |
| `L.joint_detection` | L · joint detection operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Quantum Imaging |
| Sub domain | Two-mode squeezing for target detection below shot-noise |
| Carrier | photon |
| Problem class | nonlinear_inverse |
| Solution space | binary_detection_map |
| Noise model | shot_poisson |
| Integration axis | temporal |
| Difficulty delta | 10 |
| L dag | 4.5 |

## 📡 4. Measurement Model

Existence of the recovered binary detection map is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 35); loss_and_noise_decoherence dominates the stability cliff; phase_drift and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `quantum_illumination` · **Forward operator:** `quantum_illumination_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 128 |
| W | px | 128 |
| N modes | — | 1000000 |
| Eta idler | — | 0.9 |
| Eta signal | — | 0.1 |
| Phase drift | — | 0 |
| Mode mismatch | — | 0 |
| Thermal photons per mode | — | 1 |
| Loss and noise decoherence | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 32 |
| W | px | 32 |
| N modes | — | 10000 – 1000000000 |
| Eta idler | — | 0.3 – 1.0 |
| Eta signal | — | 0.01 – 1.0 |
| Phase drift | — | 0.0 – 0.5 |
| Mode mismatch | — | 0.0 – 0.3 |
| Thermal photons per mode | — | 0.01 – 100 |
| Loss and noise decoherence | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 16.0

| Metric | Range |
|---|---|
| Psnr db | 5.0 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `700` and δ = `10`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x2e02a797d2bd1d9a544008258a6e6dd07e1ce8f075e64108972adec58d526e0d`
- **Chain tx hash:** `0xb913d3a2ba6305f5be64a49383cc78e9fd4f2a00544c0ef1be4dc31294c8e863`
- **Chain block:** `41554241`

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## File Mapping

This bundle consists of: `L1-154.md`, `L1-154.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-154.md` | Source of truth — edit this | Human or LLM |
| `L1-154.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-154`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._