# Inverse quantum measurement problem

## TL;DR

This paper investigates the conditions under which quantum amplitude phases can be reconstructed from measurement data, challenging the notion that phase information is irretrievably lost in quantum experiments.

## Contribution

It introduces a framework for determining when quantum amplitudes can be inferred from observed probability distributions and averages.

## Key findings

- Identifies conditions enabling phase recovery from measurements
- Demonstrates potential for reconstructing wave functions in experiments
- Provides theoretical insights into quantum measurement limitations

## Abstract

Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the experimental data. Yet, there are experiments which report measurements of wave functions, and closely related quantities such as Bohm's velocities and positions of bohmian particles. We invert the question, and ask under which conditions the values of quantum amplitudes can be recovered from observed probability distributions and averages.