Quantum sensing as parameter estimation
A physical parameter changes a quantum state, and a measurement converts that change into data.
$$p(x\mid\theta)=\mathrm{Tr}[M_x\rho(\theta)]$$
Physical intuition
A physical parameter changes a quantum state, and a measurement converts that change into data.
Deep dive: physical mechanism
Specify the parameter-encoding map, the initial state, a positive-operator-valued measurement and an estimator. The inverse problem is to infer the unknown parameter from a distribution of outcomes.
What is measured experimentally?
Repeated measurements yield a likelihood curve and a calibrated estimate with an uncertainty interval.
Assumptions, noise and limitations
Quantum sensitivity alone does not imply accuracy: model mismatch, drift and calibration bias can dominate.
Research and simulation exercise
Simulate binary outcomes for several parameter values and recover the parameter by maximum likelihood.
Connect the ideas
Explore the chapter overview, learning path, and references.