Convex optimization over classes of multiparticle entanglement

Abstract

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010)].

10 pages, 9 figures, 1 table, 44 references, close to the published version

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Cited by in corpus (20)

• Optimal verification of general bipartite pure states
• Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure
• Building separable approximations for quantum states via neural networks
• Hilbert-Schmidt distance and entanglement witnessing
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• A Variational Approach to the Quantum Separability Problem
• Graph-theoretic approach to Bell experiments with low detection efficiency
• Optimal approximations of available states and a triple uncertainty relation
• Coherent states of the Laguerre-Gauss modes
• Complete Optimal Convex Approximations of Qubit States under $B_2$ Distance
• Certifying Quantum Separability with Adaptive Polytopes
• Introduction to quantum entanglement in many-body systems
• Bounding the detection efficiency threshold in Bell tests using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles
• The optimal approximation of qubit states with limited quantum states
• The best approximation of an objective state with a given set of quantum states
• The best approximation of a given qubit state with the limited pure-state set
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Algorithm for evaluating distance-based entanglement measures
• Reliable optimization of arbitrary functions over quantum measurements