Generalized Bell states and principal realization of the Yangian Y(sl_N)

TL;DR

This paper demonstrates that the Yangian Y(sl_N) algebra acts simply on maximally entangled states, revealing a new quantum number J^2 that explains their properties, with implications for quantum symmetry understanding.

Contribution

It introduces a principal realization of the Yangian Y(sl_N) that simplifies its action on entangled states and computes a new quantum number J^2.

Findings

Principal generators permute maximally entangled states simply

Explicit computation of the quantum number J^2 under Yangian symmetry

Simplified description of Yangian action on tensor products

Abstract

We prove that the action of the Yangian algebra Y(sl_N) is better described by the principal generators on the tensor product of the fundamental representation and its dual. The generalized Bell states or maximally entangled states are permuted by the principal generators in a dramatically simple manner on the tensor product. Under the Yangian symmetry the new quantum number J^2 is also explicitly computed, which gives an explanation for these maximally entangled states.