Premeasurement

Premeasurement is the stage in quantum measurement during which a coupling between a system and a measuring device creates correlations between the system’s observable and the device’s pointer states. It is distinguished from the subsequent readout or collapse, which yields a definite outcome, and from any post-selection or classical record extraction.

In the standard von Neumann measurement model, an observable A has eigenstates |a_i> with eigenvalues a_i. The measuring device starts in a ready state |A0>. The measurement interaction, described by a unitary U, maps U(|a_i>⊗|A0>) = |a_i>⊗|A_i>. For a general system state |ψ> = sum_i c_i|a_i>, the joint state after premeasurement is sum_i c_i|a_i>⊗|A_i>, i.e., an entangled state that correlates each eigencomponent with a distinct pointer state. The reduced state of the system is ∑|c_i|^2|a_i><a_i|, and the apparatus carries the corresponding probability distribution. The apparatus states |A_i> are intended to become distinguishable and robust, often through decoherence.

Premeasurement is closely related to generalized measurements. Any measurement can be modeled as a premeasurement followed by a readout, with indirect measurement models producing POVMs. While the premeasurement step is unitary on the system–apparatus composite, the appearance of a definite outcome arises only after the readout or tracing over the apparatus and environment, depending on the interpretation.

Interpretationally, premeasurement does not by itself select a single result; outcome selection is associated with the subsequent observation or state update. Decoherence provides a mechanism by which the entangled correlations become effectively classical records.