Entanglement in a class of multiqubit mixed states without multipartite tangles

TL;DR

This paper investigates a class of multiqubit mixed states that are entangled without exhibiting multipartite tangles, revealing their entanglement is linked to quantum complementary relations in their purified states.

Contribution

It introduces a novel analysis connecting entanglement in mixed states without multipartite tangles to QCR entanglement in their purifications.

Findings

Entanglement relates to QCR in purified states.

Mixed states lack higher-order tangles but are still entangled.

Entanglement is a form of genuine multipartite QCR entanglement.

Abstract

Based on quantum complementary relations (QCRs) and a purification scenario, we analyze a class of N-qubit mixed states that are entangled but do not have two-, and genuine three-, four-, ..., N-qubit entanglements. It is shown that entanglement (one-tangle or negativity) in these mixed states is closely related to the QCR entanglement of their purified states. In particular, it is elaborated that when the mixed state does not have multipartite tangles (two- and higher tangles), its entanglement is actually a kind of genuine multipartite QCR entanglement between the system and its environment.