Optimal detection of entanglement in Greenberger-Horne-Zeilinger states

2010/06/30 by Alastair Kay · 36 citations
Computer Science · Mathematics · Physics and Astronomy · #Class (philosophy) #Computer science #Diagonal #Entanglement witness #Mathematics #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Squashed entanglement #Transpose #W state #quant-ph

paper · pdf · doi:10.1103/physreva.83.020303

published in Physical Review A 83(2) (American Physical Society) · 4 pages, 2 figures. v2: minor improvements. v3: negative sign corrected

arxiv created 2010/07/07 · openalex publication_date 2011/02/22 · arxiv updated 2011/02/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present a broad class of N-qubit Greenberger-Horne-Zeilinger (GHZ)-diagonal states such that nonpositivity under the partial transpose operation is necessary and sufficient for the presence of entanglement, including many naturally arising instances such as dephased GHZ states. Furthermore, our proof directly leads to an entanglement witness which saturates this bound. The witness is applied to thermal GHZ states to prove that the entanglement can be extremely robust to system imperfections.

Citations

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Experimental Detection of Multipartite Entanglement using Witness Operators
• A de Finetti representation for finite symmetric quantum states
• Classification of multiqubit mixed states: Separability and distillability properties
• Optimization of entanglement witnesses
• Detecting multipartite entanglement
• Entanglement detection

Cited by

• Detecting entanglement from few partial transpose moments and their decay via weight enumerators
• Estimating the best separable approximation of non-pure spin-squeezed states