fisher-glasses-tail-certified-metrology

name	fisher-glasses-tail-certified-metrology
description	Tail-certified quantum metrology for quenched sensors — Fisher-zero integrability transition, no-go theorem on averaged Fisher data, universal design laws (safe windows, nondegenerate portfolios, Fisher reserves, Fisher-cut criteria). Activation: quantum metrology, Fisher information, quenched environments, tail certification, NV centers, superconducting qubits, Fisher glass, QFI certification
metadata	{"arxiv_id":"2607.01085","published":"2026-07-01","authors":"El Mustapha Mansouri, Keigo Arai"}

Fisher Glasses: Tail-Certified Quantum Metrology

Overview

Quantum metrological advantage certified by averaged Fisher responses (contrast, susceptibility, QFI) fails in quenched sensors where slow environmental variables freeze within a session but vary between repetitions.

Key Contributions

No-Go Theorem

No averaged Fisher data determine quenched certification. Ensembles sharing averaged Fisher matrix, QFI, and projected information can have finite or zero certified precision.

Fisher-Zero Integrability Transition

• The inverse-loss tail exponent β sets the boundary
• Nonintegrable certified loss for β ≤ 1, even when annealed information is large or scaling
• Certified quantum resource is response transverse to latent disorder, not raw amplification

Universal Design Laws

1. Safe windows: Operating regimes where certification is reliable
2. Nondegenerate portfolios: Measurement configurations avoiding degeneracy
3. Fisher reserves: Buffer capacity for certification robustness
4. Action separation: Distinguishing signal from latent disorder
5. Fisher-cut criteria: Threshold for meaningful certification

Experimental Validation

Shallow-NV Ramsey tournament: average-QFI optimization is tail-catastrophic, whereas tail-certified designs recover nearly three orders of magnitude in certified information at equal shot budget.

Applicable Systems

• Shallow NV centers
• Superconducting qubits with slow two-level fluctuators
• Semiconductor spin qubits in drifting charge noise

Pitfalls

• Optimizing average QFI can be tail-catastrophic — use tail-certified designs instead
• The Fisher-zero rare-event statistics govern the Fisher glass phase

Related Skills

• quantum-metrology-sensing-review — broader quantum metrology review
• finite-shot-quantum-metrology — finite-measurement metrology theory
• quantum-fisher-information-duality — QFI duality framework

References

• arXiv: 2607.01085 — "Fisher Glasses: Tail-Certified Quantum Metrology in Quenched Environments"