Quantum measurement process with an ideal detector array

Abstract

Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible value of the observable. The study of this setup in the frame of von Neumann’s quantum mechanical measurement process has a remarkable result: already after the interaction of the measured system with the detector array without collapse, exactly one detector is indicating a detection. Each single detector indicates either 0 or 1 detection, and no superposition can be attributed to it.