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

Xue-Na Zhu, Gui Bao, Ming Li, Ming-Jing Zhao, Shao-Ming Fei

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.

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

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 bipartite systems. The fully entangled fractions for classes of quantum states are analytically derived. Detailed examples are given to illustrate the advantages of our results.
Paper Structure (5 sections, 6 theorems, 48 equations, 2 figures)

This paper contains 5 sections, 6 theorems, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. An alternative expression of the fully entangled fraction
  3. Bounds on the fully entangled fraction
  4. Fully entangled fraction for some classes of mixed states
  5. Conclusion

Key Result

Proposition 1

The fully entangled fraction of a state $\rho\in H_A\otimes H_B$ can be expressed as

Figures (2)

  • Figure 1: Upper bounds of $F(\rho_{a})$. The blue solid line is from Theorem \ref{['TH1']}, the red solid line is given by Corollary \ref{['c1']}, and the dashed line is obtained by Ref.huang.
  • Figure 2: Bounds of $F(\rho_{a})$. The solid line is $f(\rho_a)$, the dashed line is the upper bound from Theorem \ref{['TH1']}.

Theorems & Definitions (6)

  • Proposition 1
  • Theorem 1
  • Corollary 1
  • Theorem 2
  • Corollary 2
  • Theorem 3