Semi-definite programming and quantum information

Abstract

This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations, optimize quantum states, and design efficient quantum algorithms and protocols. The paper also discusses implementational aspects, such as solvers for SDP and modeling tools, enabling the effective employment of optimization techniques in quantum information processing. The insights and methodologies presented in this paper have proven instrumental in advancing the field of quantum information, facilitating the development of novel communication protocols, self-testing methods, and a deeper understanding of quantum entanglement. Overall, this study offers a resource for researchers interested in the intersection of optimization and quantum information, opening up new avenues for exploration and breakthroughs in this rapidly evolving field.

review and introduction to SDP in quantum information; 91 pages; comments are verrry welcome

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• Semidefinite programming relaxations for quantum correlations
• The future of secure communications: device independence in quantum key distribution
• Experimental virtual distillation of entanglement and coherence
• Generalized measurements on qubits in quantum randomness certification and expansion
• Variational Optimization for Quantum Problems using Deep Generative Networks
• Quantum Strategies for Rendezvous and Domination Tasks on Graphs with Mobile Agents
• Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
• Optimal discrimination of quantum sequences
• Bounding conditional entropy of bipartite states with Bell operators
• Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
• Virtual Quantum Markov Chains
• Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
• Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement