Constructive entanglement test from triangle inequality

TL;DR

This paper introduces a simple, experimentally accessible entanglement test for multipartite quantum states based on a new lower bound derived from the triangle inequality applied to the root infidelity distance.

Contribution

It presents a novel lower bound on the geometric measure of entanglement for mixed states using the triangle inequality, leading to practical entanglement criteria.

Findings

Provides a straightforward entanglement test applicable to multipartite systems

Derives a lower bound on geometric entanglement using the triangle inequality

Results in experimentally accessible criteria for detecting entanglement

Abstract

We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. Proposed criteria provide an experimentally accessible, powerful entanglement test.