2020/07/27 by Thiago Mureebe Carrijo, Wesley B. Cardoso, Wesley Bueno Cardoso +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Bounded function #Computer science #Convex optimization #Convex set #Discrete mathematics #Duality (order theory) #Mathematical analysis #Mathematics #Measure (data warehouse) #Physics #Plane (geometry) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Regular polygon #Tangle #physics.comp-ph #quant-ph
paper · pdf · doi:10.1103/physreva.104.022413
published in Physical Review A 104(2) (American Physical Society) · 7 pages, 4 figures
arxiv created 2020/07/27 · openalex created_date 2020/08/03 · openalex publication_date 2021/08/16 · arxiv updated 2021/08/25 · openalex updated_date 2026/08/05
We explore the dual problem of the convex roof construction by identifying it as a linear semi-infinite programming (LSIP) problem. Using the LSIP theory, we show the absence of a duality gap between primal and dual problems, even if the entanglement quantifier is not continuous, and prove that the set of optimal solutions is nonempty and bounded. In addition, we implement a central cutting-plane algorithm for LSIP to quantify entanglement between three qubits. The algorithm has global convergence property and gives lower bounds on the entanglement measure for nonoptimal feasible points. As an application, we use the algorithm for calculating the convex roof of the three-tangle and \ensuremathπ-tangle measures for families of states with low and high ranks. Since the \ensuremathπ-tangle measure quantifies the entanglement of W states, we apply the values of the two quantifiers to distinguish between the two different types of genuine three-qubit entanglement.