Quantum Entanglement and Geometry

2010/03/19 by Andreas Gabriel, Gabriel, Andreas
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1003.3778

openalex publication_date 2010/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability criteria and entanglement measures are presented. Finally, the geometry of 2x2- and 3x3-dimensional state spaces is analysed and visualised.

Citations

• NPPT Bound Entanglement Exists
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Distinguishing Separable and Entangled States
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• Die gegenw�rtige Situation in der Quantenmechanik
• On the Einstein Podolsky Rosen paradox
• Quantifying Entanglement

Related

• An Introduction to Quantum Entanglement: a Geometric Approach
• Geometric measure of entanglement for multipartite quantum states
• Quantum entanglement: geometric quantification and applications to multi-partite states and quantum phase transitions
• An elementary introduction to the geometry of quantum states with pictures
• A Geometry of entanglement and entropy