Multipartite Entanglement Criterion from Uncertainty Relations

TL;DR

This paper introduces a new entanglement detection criterion combining positive partial transpose operations with uncertainty relations, applicable to various quantum states and outperforming existing criteria like Bell inequalities.

Contribution

It presents a novel entanglement criterion based on uncertainty relations and partial transpose, effective for bipartite and multipartite states, including continuous variable systems.

Findings

Detects all pure entangled bipartite and tripartite states

Outperforms Bell inequalities and other criteria

Applicable to continuous variable and angular momentum states

Abstract

We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be detected by experimentally measuring mean values and variances of specific observables. Those observables must satisfy a specific condition in order to be used, and we show their general form in the $2\times 2$ (two qubits) dimension case. The criterion is applied on a variety of physical systems including bipartite and multipartite mixed states and reveals itself to be stronger than the Bell inequalities and other criteria. The criterion also work on continuous variable cat states and angular momentum states of the radiation field.