Is monogamy of entanglement geometrical?

Abstract

This work aims to understand the monogamy of quantum entanglement from a geometrical point of view. By regarding quantum entanglement as a geometrical structure on the state space of quantum systems and attributing all entanglement related properties as emergent from this geometry of entanglement, we assume there exists a genuine general monogamous relation of quantum entanglement w.r.t. a correspondent genuine entanglement measure Q* which possesses an underlying geometrical origin. We speculate that the monogamous relations w.r.t. an entanglement measure Q can be understood by comparing the different dimension dependencies of the measure Q and Q*. We gave evidences of our conjecture by readdressing two observed properties of the monogamy relations from this geometrical standpoint. Besides the phenomenal explanation of the monogamy of entanglement, we also discussed a fibre bundle structure based candidate solution for the geometry of entanglement and explained how this idea is related to the ER=EPR conjecture and other interesting quantum information processing problems including monogamy of entanglement, entanglement distillation, bound entanglement and activation, and entanglement catalyst.

arXiv comment23 pages, 8 figures

References in corpus (24)

• Quantum entanglement
• The classical-quantum boundary for correlations: discord and related measures
• Entanglement Measures and Purification Procedures
• Building up spacetime with quantum entanglement
• Unified View of Quantum and Classical Correlations
• Holographic Entanglement Entropy: An Overview
• Complexity and Shock Wave Geometries
• Area laws in quantum systems: mutual information and correlations
• Monogamy of entanglement and other correlations
• Bound entanglement can be activated
• Are general quantum correlations monogamous?
• Geometry of entangled states, Bloch spheres and Hopf fibrations
• The holographic dual of an EPR pair has a wormhole
• Switchbacks and the Bridge to Nowhere
• The geometry of entanglement: metrics, connections and the geometric phase
• The twistor geometry of three-qubit entanglement
• Geometry of the 3-Qubit State, Entanglement and Division Algebras
• Microscopic wormholes and the geometry of entanglement
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Are entangled particles connected by wormholes? Support for the ER=EPR conjecture from entropy inequalities
• New Concepts for Old Black Holes
• What does monogamy in higher powers of a correlation measure mean?
• Bound on distributed entanglement
• Segre variety, conifold, Hopf fibration, and separable multi-qubit states