On the Algorithmic Content of Quantum Measurements

TL;DR

This paper demonstrates that most pure quantum states yield negligible information from measurements, highlighting fundamental limits on extracting meaningful data from quantum systems regardless of measurement outcomes.

Contribution

It reveals that for most pure states, quantum measurements produce essentially no meaningful information, emphasizing inherent limitations due to conservation laws.

Findings

Most pure states produce no meaningful measurement information.

The result holds regardless of the number of measurement outcomes.

Conservation inequalities prevent processing of measurement noise into coherent data.

Abstract

We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced. This is independent of the number of outcomes of the quantum measurement. Due to conservation inequalities, such random noise cannot be processed into coherent data.