2019/03/31 by Zhaohui Wei, Lijinzhi Lin · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Discrete mathematics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum metrology #Statistical physics #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1103/physreva.103.032215
published in Physical Review A 103(3) (American Physical Society) · A mathematical characterization for nondegeneracy Bell inequalities that proves quite a lot of well-known Bell inequalities are nondegenerate was added; A demonstration of our approach that quantifies the entanglement of qutrit-qutrit states based on their violation to the CGLMP inequality was also provided; Comments are welcome
openalex created_date 2019/03/22 · arxiv created 2019/12/04 · openalex publication_date 2021/03/17 · arxiv updated 2021/03/24 · openalex updated_date 2026/08/05
We define a property called nondegeneracy for Bell inequalities, which describes the situation that in a Bell setting, if a Bell inequality and involved local measurements are fixed, any quantum state with a given dimension and its orthogonal quantum state cannot violate remarkably the inequality simultaneously. By choosing a proper nondegenerate Bell inequality, we prove that for an unknown bipartite quantum state of given dimension, based on the measurement statistics only, we can provide an analytic lower bound for the entanglement of formation or even the distillable entanglement, making the whole process semi device independent. We characterize the mathematical structure of nondegeneracy, and prove that quite a lot of well-known Bell inequalities are nondegenerate. We demonstrate our approach by quantifying entanglement for qutrit-qutrit states based on their violations of the Collins-Gisin-Linden-Masser-Popescu inequality.