Maximal Entanglement via Collective Coordinates

TL;DR

This paper introduces a new class of maximally entangled states for prime-dimensional Hilbert spaces, using collective coordinate frameworks that relate to phase space concepts, enhancing understanding of entanglement structures.

Contribution

It presents a novel construction of MES states based on collective coordinates, linking them to phase space analogies and generalizing the Mean King Problem.

Findings

Constructed MES states using collective coordinates.

Established a phase space analogy for entangled states.

Extended the Mean King Problem to new MES frameworks.

Abstract

Maximal entangled states (MES) provide a basis to 2d-dimensional particles Hilbert space, d=prime $\ne2$. These states allow generalization of the Mean King Problem. The states may be viewed as build of points each underpins a product state carrying a mutual unbiased bases (MUB) label or, alternatively, as product states labeled with center of mass and relative coordinates. The coordinate-like label of the center of mass and the momentum-like of the relative coordinates provides a MES account of the Hilbert space in close analogy with the single particle phase space coordinates.