Metrological Detection of Multipartite Entanglement from Young Diagrams

TL;DR

This paper introduces a novel method for detecting and characterizing multipartite entanglement using Young diagrams, linking their shape to quantum metrological usefulness, and demonstrates experimental applicability with existing atomic data.

Contribution

It develops entanglement witnesses based on Young diagram shapes and identifies Dyson's rank as a quantum resource, integrating entanglement quantifiers within this framework.

Findings

Young diagrams effectively characterize entanglement structure.

Dyson's rank serves as a resource for quantum metrology.

Method is experimentally feasible with existing atomic data.

Abstract

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and $k$-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients.