The library computes arbitrary monotone quantum Fisher information matrices (the full alpha-z family, validated to ~1e-7 against finite differences of the divergence). That is exactly the object a quantum Cramer-Rao bound needs, so a metrology layer is mostly a thin wrapper over work already done.
What to do
A qbm/metrology.py providing, for a QBM used as a probe state:
- the CR bound
Cov(theta_hat) >= I(theta)^-1 / N for a chosen metric
- single-parameter bounds and the multi-parameter matrix version
- a helper for the attainability gap between SLD (Fisher-Bures) and other members of the family, which is where the physics is
Why it is interesting
Thermal states as metrological probes is an active topic, and the alpha-z family lets you ask which geometry gives the tightest bound for a given estimation problem — a question the library can answer but currently does not expose.
Acceptance
- reproduce a known single-qubit thermometry bound analytically
- a notebook or example demonstrating a bound and a saturating estimator
The library computes arbitrary monotone quantum Fisher information matrices (the full alpha-z family, validated to ~1e-7 against finite differences of the divergence). That is exactly the object a quantum Cramer-Rao bound needs, so a metrology layer is mostly a thin wrapper over work already done.
What to do
A
qbm/metrology.pyproviding, for a QBM used as a probe state:Cov(theta_hat) >= I(theta)^-1 / Nfor a chosen metricWhy it is interesting
Thermal states as metrological probes is an active topic, and the alpha-z family lets you ask which geometry gives the tightest bound for a given estimation problem — a question the library can answer but currently does not expose.
Acceptance