# Position measurement-induced collapse states: Proposal of an experiment

## TL;DR

This paper proposes an experiment using a modified optical setup to test the existence of position measurement-induced collapse states, aiming to deepen understanding of wave function collapse in quantum mechanics.

## Contribution

It introduces a novel experimental design with a modified Lloyd's mirror to observe PMIC states and their diffraction patterns, including quantum fractal structures.

## Key findings

- Predicted diffraction patterns exhibit quantum fractal structures called 'quantum carpets'
- Time evolution of PMIC states shows Fresnel and Fraunhofer diffraction patterns
- The experiment could validate the PMIC formalism and enhance understanding of wave function collapse

## Abstract

The quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the `position measurement-induced collapse' (PMIC) states. An experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd's mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called `quantum carpets', first discovered by Berry (1996). The PMIC formalism in this case closely follows the `boundary bound diffraction' analysed in a previous work by Tounli, Alverado and Sanz (2019). In addition to obtaining their results, we have shown that the time evolution of these collapsed states also leads to Fresnel and Fraunhofer diffractions. It is anticipated that the verification of PMIC states by this experiment will help to better understand collapse of the wave function during quantum measurements.