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Xue-Na Zhu

Publications and source records attributed to Xue-Na Zhu.

At least 19 recordsLinked to original sources
arXiv2026

Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems

The monogamy relations characterize the distribution of quantum correlations among the multipartite quantum systems. We study the monogamy relations of the entanglement of assistance in $2\otimes 2\otimes d$ systems. We present explicitly the relations satisfied by the concurrence, the tangle and the concurrence of assistance, which can be used to derive rigorous monogamy relations. Detailed examples are given to illustrate our results.

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arXiv2026

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.

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arXiv2024

Classifying coherence with a finite set of witnesses

Coherence is a fundamental resource in quantum information processing, which can be certified by a coherence witness. In order to detect all the coherent states, we introduce a useful concept of coherence witness and structure the set of coherence witnesses $C^{d}_{[m,M]}$. We present necessary and sufficient conditions of detecting quantum coherence of $d-$dimensional quantum states based on $C^{d}_{[m,M]}$. Moreover, we show that each coherent state can be detected by one of the coherence witnesses in a finite set. The corresponding finite set of coherence witnesses is presented explicitly, which detects all the coherent states.

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arXiv2023

Polygamy relation of quantum correlations with equality

We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, we present polygamy inequalities satisfied by the $β$th $(β>0)$ power of the quantum correlation measures. Taking concurrence of assistance as an example, we further illustrate the significance and advantages of these relations. We also obtain a polygamy relation with equality by considering the one-to-group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. We demonstrate that such relations for tripartite states can be generalized to multipartite systems.

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arXiv2023

Monogamy of entanglement for tripartite systems

We study the monogamy of arbitrary quantum entanglement measures $E$ for tripartite quantum systems. Both sufficient and necessary conditions for $E$ to be monogamous in terms of the $α$th power of $E$ are explicitly derived. It is shown that such monogamy of a entanglement measure $E$ only depends on the boundedness of the solution set of certain equations. Moreover, the monogamy conditions have been also obtained with respect to certain subsets of quantum states for a given quantum correlation. Detailed examples are given to illustrate our results.

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arXiv2023

A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices

We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{αβ}(ρ)$ and $W_{ab,αβ}(ρ)$ constructed from the correlation tensors in the Bloch representation. These separability criteria can be simplified and detect more entanglement than the previous separability criteria. Detailed examples are given to illustrate the advantages of results.

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arXiv2018

Monogamy properties of qubit systems

We investigate monogamy relations related to quantum entanglement for $n-$qubit quantum systems. General monogamy inequalities are presented to the $β$th $(β\in(0,2))$ power of concurrence, negativity and the convex-roof extended negativity, as well as the $β$th $(β\in(0,\sqrt{2}))$ power of entanglement of formation. These monogamy relations are complementary to the existing ones with different regions of parameter $β$. In additions, new monogamy relations are also derived which include the existing ones as special cases.

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arXiv2018

Analytical Expression of Quantum Discord for Rank-2 Two-qubit States

Quantum correlations characterized by quantum entanglement and quantum discord play important roles in many quantum information processing. We study the relations among the entanglement of formation, concurrence, tangle, linear entropy based classical correlation and von Neumann entropy based classical correlation. We present analytical formulae of linear entropy based classical correlation for arbitrary $d\otimes 2$ quantum states and von Neumann entropy based classical correlation for arbitrary $2\otimes 2$ rank-2 quantum states. From the von Neumann entropy based classical correlation, we derive an explicit formula of quantum discord for arbitrary rank-2 two-qubit quantum states.

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arXiv2017

A lower bound of concurrence for multipartite quantum systems

We present a lower bound of concurrence for four-partite systems in terms of the concurrence for $M\, (2\leq M\leq 3)$ part quantum systems and give an analytical lower bound for $2\otimes2\otimes2\otimes2$ mixed quantum sates. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. Furthermore, our approach can be generalized to multipartite quantum systems.

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arXiv2017

Lower bound of multipartite concurrence based on sub-multipartite quantum systems

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems.

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arXiv2017

Monogamy relations of concurrence for any dimensional quantum systems

We study monogamy relations for arbitrary dimensional multipartite systems. Monogamy relations based on concurrence and concurrence of assistance for any dimensional $m_1\otimes m_2\otimes...\otimes m_{N}$ quantum states are derived, which give rise to the restrictions on the entanglement distributions among the subsystems. Besides, we give the lower bound of concurrence for four-partite mixed states. The approach can be readily generalized to arbitrary multipartite systems.

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arXiv2015

Generalized Monogamy Relations of Concurrence for N-qubit Systems

We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $ABC_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $ABC_1$ and $C_2...C_{N-2}$ are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.

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arXiv2014

Lower Bound of Concurrence for Qubit Systems

We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. The approach is generalized to arbitrary qubit systems.

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arXiv2013

One-way Unlocalizable Information Deficit

We introduce one-way unlocalizable information deficit with respect to the one-way information deficit, similar to the definition of one-way unlocalizable quantum discord with respect to one-way quantum discord. The properties of the one-way unlocalizable information deficit and the relations among one-way unlocalizable information deficit, one-way unlocalizable quantum discord, one-way quantum discord, one-way information deficit and other quantum correlations are investigated. Analytical formulas of the one-way unlocalizable quantum discord are given to detailed examples.

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arXiv2012

Improved lower and upper bounds for entanglement of formation

We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed examples are presented.

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