PHY.9:4.3 - Construct the preparation and comparison

Specify how the subject, probe and reference are prepared before coupling. Then choose what is held fixed, what is varied and what is read. Include the order when the first interaction changes the next state.

Use a differential, reversed, ratio or null comparison when its physical invariance removes a consequential influence. Derive the cancellation from the arrangement. For example, reversing a known applied force while preserving a common force offset changes the wanted response but leaves the offset shared. A reversal that also changes the offset does not support that subtraction.

For a quantum probe, choose a prepared state, the parameter-dependent interaction and the measurement together. The physical interaction may be described by a channel taking rho to rho_theta; measurement operators E_k give outcome probabilities P(k|theta)=Tr(rho_theta E_k). Here rho is the prepared state, theta the sought parameter, and the positive operators E_k sum to the identity. If those probabilities do not change with theta, that preparation and readout supply no information about it.

A reference can also select which part of a response is read. A phase-sensitive measurement needs a phase reference; a differential displacement needs a reference position. Preserve the conditions that make this reference stable during the comparison.