Finding maximal quantum resources

TL;DR

This paper introduces an algorithmic approach to identify maximally resourceful quantum states across various applications, providing insights into entanglement and resource quantification in multipartite systems.

Contribution

It presents a versatile method for finding maximally resourceful states for different quantum resources and applications, including entanglement measures and network preparation.

Findings

Identified physically interesting maximally resourceful states.

Provided insights into absolutely maximally entangled states.

Demonstrated universality across multiple quantum resource measures.

Abstract

For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum states are often regarded as resourceful. We propose an algorithmic method to find maximally resourceful states of several particles for various applications and quantifiers. We discuss in detail the case of the geometric measure, identifying physically interesting states and delivering insights to the problem of absolutely maximally entangled states. Moreover, we demonstrate the universality of our approach by applying it to maximally entangled subspaces, the Schmidt-rank, the stabilizer rank as well as the preparability in triangle networks.