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 (24)

• Separability Criterion for Density Matrices
• Quantum information with continuous variables
• Separability of Mixed States: Necessary and Sufficient Conditions
• Three qubits can be entangled in two inequivalent ways
• Entanglement of Orbital Angular Momentum States of Photons
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Measures and dynamics of entangled states
• Violation of local uncertainty relations as a signature of entanglement
• Entanglement conditions for two-mode states
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Inseparability criteria for bipartite quantum states
• Detection of entanglement with few local measurements
• Characterizing the entanglement of bipartite quantum systems
• Inseparability inequalities for higher-order moments for bipartite systems
• Multipartite bound entangled states that violate Bell's inequality
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebra: detection of non-Gaussian entangled states
• Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation
• Existence of the Schmidt decomposition for tripartite systems
• Quantification of entanglement via uncertainties
• Multi-Partite Entanglement Inequalities via Spin Vector Geometry
• Entanglement conditions for tripartite systems via indeterminacy relations

Cited by in corpus (9)

• Detecting mixedness of qutrit systems using the uncertainty relation
• Stronger steerability criterion for more uncertain continuous variable systems
• Entanglement criteria and nonlocality for multi-mode continuous variable systems
• Fine-grained uncertainty relation and nonlocality of tripartite systems
• Hierarchies of multipartite entanglement for continuous-variable states
• Detecting non-Markovianity via uncertainty relations
• Uncertainty relation and inseparability criterion
• Geometric uncertainty relation for quantum ensembles
• Separability bounds on multiqubit moments due to positivity under partial transpose