Systematic Construction of Genuine Multipartite Entanglement Criteria using Uncertainty Relations

Abstract

A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive partial transpose criterion of separability, and quantum mechanical uncertainty relations. As a consequence, each criterion encountered consists of a single inequality that is nicely computable and experimentally feasible, and that when violated is sufficient condition for genuine multipartite entanglement. Additionally we show that the previous work of van Loock and Furusawa [Phys. Rev. A, 67, 052315 (2003)] is a special case of our result that includes strongest criteria to detect entanglement.

15 pages, 2 tables and 1 figure

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• Detecting entanglement of continuous variables with three mutually unbiased bases
• Uncertainty Relations for coarse-grained measurements: an overview
• Relating spin squeezing to multipartite entanglement criteria for particles and modes
• Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables
• Spin-orbit-coupled quantum memory of a double quantum dot
• Uncertainty relations for characteristic functions
• Preparational Uncertainty Relations for $N$ Continuous Variables
• Quantifying Tripartite Spatial and Energy-Time Entanglement in Nonlinear Optics
• Minimal criteria for continuous-variable genuine multipartite entanglement
• Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries
• Sufficient Wigner Negativity Implies Genuine Multipartite Entanglement
• Multipartite spatial entanglement generated by concurrent nonlinear processes