When is a set of questions to nature together with sharp answers to those questions in one-to-one correspondence with a set of quantum states?

TL;DR

This paper investigates conditions under which a set of questions and their precise answers correspond uniquely to quantum states, providing affirmative answers in specific physical and symmetry contexts.

Contribution

It offers a theoretical framework linking question-answer sets to quantum states, with new results for spin/angular momentum and symmetry scenarios.

Findings

Affirmative correspondence for spin/angular momentum cases

Results under certain symmetry assumptions

Partial results applicable to quantum state identification

Abstract

A general question is posed to the quantum community. Partial results are formulated in a self-contained way. In particular, the title question is answered affirmatorily in two cases: 1) The case of spin/ angular momentum of a partcle; 2) A general symmetry situation under certain technical assumptions.