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.

中文翻译：

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半定规划和量子信息

本文对量子信息背景下的半定规划（SDP）技术进行了全面的探索。它研究了凸优化、对偶性和 SDP 公式的数学基础，为解决量子系统中的优化挑战提供了坚实的理论框架。通过利用这些工具，研究人员和从业者可以表征经典和量子相关性、优化量子态并设计高效的量子算法和协议。本文还讨论了实现方面，例如 SDP 求解器和建模工具，从而能够在量子信息处理中有效利用优化技术。事实证明，本文提出的见解和方法有助于推动量子信息领域的发展，促进新型通信协议、自测试方法的开发以及对量子纠缠的更深入理解。