Platonic Entanglement

TL;DR

This paper constructs highly entangled quantum states on platonic solid topologies using tensor networks and AME states, revealing their entropy properties and connection to Reed-Solomon codes.

Contribution

It introduces a novel method to build entangled states on platonic solids leveraging AME states and explores their entropy and algebraic properties.

Findings

Entangled states on platonic solids have integer and near-maximal entropy.

All platonic solids can host AME states based on Reed-Solomon codes.

The construction links geometric topology with quantum entanglement properties.

Abstract

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.