2019/02/21 by Qi Zhao, Gerui Wang, Xiao Yuan +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Dimension (graph theory) #Entanglement witness #Mathematics #Multipartite #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Robustness (evolution) #Separable state #Squashed entanglement #Telecommunications #W state #White noise #Witness #quant-ph
paper · pdf · doi:10.1103/physreva.99.052349
published as Phys. Rev. A 99, 052349 (2019) · 8 pages, 1 figure
arxiv created 2019/02/21 · openalex publication_date 2019/05/28 · arxiv updated 2019/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Entanglement is a key resource for quantum information processing. A widely used tool for detecting entanglement is the entanglement witness, where the measurement of the witness operator is guaranteed to be positive for all separable states and can be negative for certain entangled states. In reality, due to exponentially increasing the Hilbert-space dimension with respect to the system size, it is very challenging to construct an efficient entanglement witness for general multipartite entangled states. For N-partite Greenberger-Horne-Zeilinger (GHZ)-like states, the most robust witness scheme requires N+1 local measurement settings and can tolerate up to 1/2 white noise. As a comparison, the most efficient witness for GHZ-like states only needs two local measurement settings and can tolerate up to 1/3 white noise. There is a tradeoff between the realization efficiency, the number of measurement settings, and the detection robustness, the maximally tolerable white noise. In this paper, we study this tradeoff by proposing a family of entanglement witnesses with k (2\ensuremath≤k\ensuremath≤N+1) local measurement settings. Considering symmetric local measurements, we calculate the maximal tolerable noise for any given number of measurement settings. Consequently, we design the optimal witness with a minimal number of settings for any given level of white noise. Our theoretical analysis can be applied to other multipartite entangled states with a strong symmetry. Our witnesses can be easily implemented in experiment and applied in practical multipartite entanglement detection under different noise conditions.