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.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.

quant-pharXiv:2602.21471Physics Letters AFeb 26, 20260 citations

Comparison of quantum discord and fully entangled fraction of two classes of $d\otimes d^2$ statesComparison of quantum discord and fully entangled fraction of two classes of $d\otimes d^2$ states

Javad Behdani, Seyed Javad Akhtarshenas, Mohsen Sarbishaei

The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the $d\otimes d$ Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the $d\otimes d$ Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.

arXiv:1604.06870Apr 23, 20160 citations

Symmetric quantum discord for a two-qubit state

王仲宵, 王波波

中国物理B：英文版Jan 1, 20140 citations

Quantifying quantum discord and entanglement of formation via unified purifications

Li-Xiang Cen, Xin-Qi Li, Jiushu Shao +1 more

We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in the purification of different states. This approach enables us to achieve analytical expressions of the two measures for some quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank- $2$ mixed states of $4\ifmmode\times\else\texttimes\fi{}2$ systems. Moreover, we apply the scheme to characterize fully the dynamic behavior of quantum correlations for the specified physical systems under decoherence.We propose a scheme to evaluate the amount of quantum discord and entanglement of formation for mixed states and reveal their ordering relation via an intrinsic relationship between the two quantities distributed in the purification of different states. This approach enables us to achieve analytical expressions of the two measures for some quantum states, such as an arbitrary two-qubit density matrix reduced from pure three-qubit states and a class of rank-$2$ mixed states of $4\ifmmode\times\else\texttimes\fi{}2$ systems. Moreover, we apply the scheme to characterize fully the dynamic behavior of quantum correlations for the specified physical systems under decoherence.

arXiv:1006.4727Physical Review AMay 17, 201155 citations

A study on quantum discord in Gaussian states

Xiong Yang, Guo Hui Huang, Mao Fa Fang

Optics CommunicationsNov 25, 20149 citations

Comparison of quantum discord and fully entangled fraction of two classes of

d\otimes d^2

d ⊗ d 2 states

On fully entangled fraction of arbitrary

d\otimes d

quantum states

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.

Comparison of quantum discord and fully entangled fraction of two classes of

d\otimes d^2

states

d\otimes d

Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.

2

mixed states of $4\ifmmode\times\else\texttimes\fi{}2$ systems. Moreover, we apply the scheme to characterize fully the dynamic behavior of quantum correlations for the specified physical systems under decoherence.