Is monogamy of entanglement geometrical?

TL;DR

This paper explores the monogamy of quantum entanglement through a geometric framework, proposing that entanglement properties emerge from an underlying geometry and relating this to various quantum information phenomena.

Contribution

It introduces a geometric perspective on entanglement monogamy, proposing a genuine monogamous measure with geometric origins and connecting it to broader quantum information concepts.

Findings

Evidence supporting the geometric interpretation of monogamy relations.

Proposed a fibre bundle structure as a candidate geometry of entanglement.

Linked geometric entanglement concepts to ER=EPR and other quantum information problems.

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.