◇Quantum Metrology Foundations

A physical parameter changes a quantum state, and a measurement converts that change into data.

The slope of a probability distribution relative to its noise determines information about a parameter.

Repeated independent measurements improve precision as the square root of sample count.

The probe state sets a measurement-independent upper limit on extractable local information.

Independent probes usually average down uncorrelated noise with shot-number scaling.

Correlated quantum probes can improve ideal phase sensitivity relative to independent probes.

A superposition accumulates relative phase while freely evolving.

A qubit sensor is a rotating state vector whose direction encodes the signal.