Linear semi-infinite programming approach for entanglement quantification

• URL: http://arxiv.org/abs/2007.13818v1
• Date: Mon, 27 Jul 2020 19:12:29 GMT
• Title: Linear semi-infinite programming approach for entanglement quantification
• Authors: Thiago Mureebe Carrijo, Wesley Bueno Cardoso, and Ardiley Torres Avelar
• Abstract summary: We show the absence of a duality gap between primal and dual problems, even if the entanglement quantifier is not continuous. We implement a central cutting-plane algorithm for LSIP to quantify entanglement between three qubits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 non-empty 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 non-optimal feasible points. As an application, we use the algorithm for calculating the convex roof of the three-tangle and $\pi$-tangle measures for families of states with low and high ranks. As the $\pi$-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.

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