# Quantum advantage by relational queries about physically realizable equivalence classes

## TL;DR

This paper explores how relational quantum queries can efficiently distinguish between classes of mutually exclusive cases without full resolution, and reviews recent progress in certifying quantum value indeterminacy for randomness generation.

## Contribution

It introduces the concept of using relational queries to partition cases and reviews advances in quantum value indeterminacy certification for quantum oracles.

## Key findings

- Relational quantum queries can effectively classify mutually exclusive cases.
- Recent progress has been made in certifying quantum value indeterminacy.
- Quantum oracles for randomness can be built based on these certifications.

## Abstract

Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive elementary cases is effectively partitioned into equivalence classes pertinent to the respective query. In the second part of the paper, we review recent progress in theoretical certifications (relative to the assumptions made) of quantum value indeterminacy as a means to build quantum oracles for randomness.