A Curious Geometrical Fact About Entanglement

TL;DR

This paper explores a geometric property of maximally entangled quantum states, revealing they form a minimal Lagrangian submanifold within the phase space of pure states, hinting at deeper physical significance.

Contribution

It identifies a novel geometric structure of maximally entangled states as a minimal Lagrangian submanifold, offering new insights into quantum entanglement geometry.

Findings

Maximally entangled states form a minimal Lagrangian submanifold.

Pure quantum states can be viewed as a phase space.

Potential physical interpretation of this geometric property.

Abstract

I sketch how the set of pure quantum states forms a phase space, and then point out a curiousity concerning maximally entangled pure states: they form a minimal Lagrangian submanifold of the set of all pure states. I suggest that this curiousity should have an interesting physical interpretation.