Multipartite Entanglement Criterion from Uncertainty Relations

Abstract

We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schrödinger-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.

5 pages

References in corpus (5)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation
• Multi-Partite Entanglement Inequalities via Spin Vector Geometry
• Entanglement conditions for tripartite systems via indeterminacy relations

Cited by in corpus (1)

• Separability bounds on multiqubit moments due to positivity under partial transpose