Entanglement detection via third-order local invariants from randomized measurements

TL;DR

This paper introduces third-order local invariants obtained from randomized measurements to improve entanglement detection in multipartite quantum states, surpassing traditional second-order criteria with more feasible protocols.

Contribution

It derives experimentally accessible third-order invariants for entanglement detection, extending capabilities beyond second-order spectral criteria in multipartite systems.

Findings

Third-order invariants detect entanglement in Werner states at lower p values.

The method surpasses second-order criteria in sensitivity.

Protocols are more feasible than full quantum state tomography.

Abstract

We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite states with arbitrary local dimensions. The results show that third-order invariants capture inter-subsystem correlations beyond second-order spectral criteria within more feasible entanglement detection protocols than full tomography. As an example, Werner states in $d=3$ the entanglement is detected for $p>\frac 12$ at the second-order correlations, and it is improved to $p>\frac 1{\sqrt[3]{10}}$ at the third-order.