Maximally entangled gluons for any $x$

TL;DR

This paper applies quantum information concepts to describe gluons inside unpolarized hadrons as maximally entangled states across all momentum fractions, revealing new insights into their quantum structure.

Contribution

It generalizes the entanglement description of gluons from small-$x$ to all $x$ values, modeling gluons as entangled qubit-qutrit systems using quantum information tools.

Findings

Gluons can be modeled as maximally entangled states for all $x$

Explicit computation of the conditional probability distribution $P(l^z|s^z)$ as a function of $x$

Extension of entanglement concepts to gluons beyond the small-$x$ regime

Abstract

Individual quarks and gluons at small-$x$ inside an unpolarized hadron can be regarded as Bell states in which qubits in the spin and orbital angular momentum spaces are maximally entangled. Using the machinery of quantum information science, we generalize this observation to all values $0<x<1$ and describe gluons (but not quarks) as maximally entangled states between a qubit and a qudit. We introduce the conditional probability distribution $P(l^z|s^z)$ of a gluon's orbital angular momentum $l^z$ given its helicity $s^z$. Restricting to the three states $l^z=0,\pm 1$, which constitute a qutrit, we explicitly compute $P$ as a function of $x$