L1 ⚛ L1-155 ⊙ Testnet

Entangled-Photon Microscopy (N00N / SPDC imaging)

Quantum Imaging · Phase sensitivity beyond shot-noise via N-photon entanglement

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⬇ L1-155.md

# ⚛ L1 Principle — Entangled-Photon Microscopy (N00N / SPDC imaging) **ID:** `L1-155` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Imaging — *Phase sensitivity beyond shot-noise via N-photon entanglement* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D phase > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554241 --- ## 🧠 1. Introduction **Entangled-Photon Microscopy (N00N / SPDC imaging)** is a **nonlinear inverse problem** whose unknown lives in **2D phase** space, within the **Phase sensitivity beyond shot-noise via N-photon entanglement** sub-domain of **Quantum Imaging**. Measurements consist of photons collected by an optical detector via a **entangled photon imaging** sensing mechanism. The forward operator applies, in order: L · spdc source operator; L · n photon interference operator; D · coincidence count operator; integration over the solid angle of incidence/emission. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 2D phase 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 ~= 30); photon_loss dominates the stability cliff; mode_coupling_efficiency 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 · spdc source → L · n photon interference → D · coincidence count → Angular integration → **y** (detector). ``` y = ∫dΩ `D.coincidence_count` `L.n_photon_interference` `L.spdc_source` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.spdc_source` | L · spdc source operator | | `L.n_photon_interference` | L · n photon interference operator | | `D.coincidence_count` | D · coincidence count operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Imaging | | Sub domain | Phase sensitivity beyond shot-noise via N-photon entanglement | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_phase | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 10 | | L dag | 4.5 | ## 📡 4. Measurement Model Existence of the recovered 2D phase 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 ~= 30); photon_loss dominates the stability cliff; mode_coupling_efficiency 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:** `entangled_photon_microscopy` · **Forward operator:** `entangled_photon_microscopy_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | N photons | photons | 2 | | Photon loss | — | 0.3 | | N coincidences | — | 100000 | | Phase instability | — | 0 | | Detector dark counts | — | 0.01 | | Mode coupling efficiency | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | N photons | photons | 2 – 10 | | Photon loss | — | 0.0 – 0.9 | | N coincidences | — | 1000 – 100000000 | | Phase instability | — | 0.0 – 0.5 | | Detector dark counts | — | 0.0 – 1.0 | | Mode coupling efficiency | — | 0.1 – 1.0 | ## 🎯 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 = `600` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2462745509ce83bcf98cd62c882c8843238dd7818bf8c2aef6892b03fdd06d09` - **Chain tx hash:** `0x6a186a8078f676549c0981d4dd7c97fbd2449fcdc2187a16981c6389b131f0d5` - **Chain block:** `41554241` --- ## File Mapping This bundle consists of: `L1-155.md`, `L1-155.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-155.md` | Source of truth — edit this | Human or LLM | | `L1-155.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 `L1-155`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-155.md).
Regenerate L1-155.json so every field matches the Markdown.
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L2-155-001 Entangled-Photon Microscopy (N00N / SPDC imaging) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x6a186a8078f676549c0981d4dd7c97fbd2449fcdc2187a16981c6389b131f0d5",
  "domain": "Quantum Imaging",
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    "title": "Entangled-Photon Microscopy (N00N / SPDC imaging)"
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      "W": 64,
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Phase sensitivity beyond shot-noise via N-photon entanglement",
  "title": "Entangled-Photon Microscopy (N00N / SPDC imaging)"
}

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