On fully entangled fraction of arbitrary $d\otimes d$ quantum states

TL;DR

This paper investigates the fully entangled fraction of bipartite quantum states using the Bloch representation, providing analytical bounds and explicit formulas for various classes of states.

Contribution

It introduces new analytical upper bounds and formulas for the fully entangled fraction of arbitrary $d\otimes d$ quantum states based on their Bloch representation.

Findings

Derived analytical upper bounds for the fully entangled fraction.

Explicit formulas for specific classes of $d\otimes d$ states.

Illustrative examples demonstrating the effectiveness of the bounds.

Abstract

We study the fully entangled fraction of quantum states based on the Bloch representation of density matrices. Analytical upper bounds on the fully entangled fraction are obtained for arbitrary $d\otimes d$ bipartite systems. The fully entangled fractions for classes of $d\otimes d$ quantum states are analytically derived. Detailed examples are given to illustrate the advantages of our results.