Pointers for Quantum Measurement Theory

Jay Lawrence

Published 2022-03-21Version 1

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a $d$-state particle we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the $d$ possible outcomes. We show that the unitary dynamics of the premeasurement process restricts the detector outputs to the subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states.