Quantum Entanglement with Geometric Measures

• URL: http://arxiv.org/abs/2506.11453v1
• Date: Fri, 13 Jun 2025 04:05:03 GMT
• Title: Quantum Entanglement with Geometric Measures
• Authors: Xuanran Zhu,
• Abstract summary: This thesis extends the geometric measure of entanglement (GME) to introduce and investigate a suite of monotone entanglements tailored for diverse quantum contexts.<n>These monotones are applicable to both bipartite and multipartite systems, offering a unified framework for characterizing entanglement across various scenarios.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to introduce and investigate a suite of GME-based entanglement monotones tailored for diverse quantum contexts, including pure states, subspaces, and mixed states. These monotones are applicable to both bipartite and multipartite systems, offering a unified framework for characterizing entanglement across various scenarios. Notably, the proposed monotones are adept at identifying entanglement with varying entanglement dimensionalities, making them particularly effective for detecting high-dimensional entanglement. To support practical computation, we develop a non-convex optimization framework that yields accurate upper bounds, complemented by semidefinite programming techniques to establish robust lower bounds. Together, these approaches provide a consistent and efficient computational methodology. This work advances both the theoretical understanding and algorithmic tools for entanglement quantification, contributing to the study of complex quantum correlations in entangled systems.

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