Parameterized genuine multipartite entanglement measure based on $\alpha$ -concurrenceParameterized genuine multipartite entanglement measure based on $$\alpha$$-concurrence

Rui-Zhou Liang, Zhi‐Xiang Jin, Wei Chen +1 more

The European Physical Journal PlusSep 19, 20250 citations

A new entanglement measure based on the total concurrence

Dong-Ping Xuan, Zhong-Xi Shen, Wen Zhou +2 more

Quantum entanglement is a crucial resource in quantum information processing, advancing quantum technologies. The greater the uncertainty in subsystems' pure states, the stronger the quantum entanglement between them. From the dual form of $q$ -concurrence ( $q\geq 2$ ) we introduce the total concurrence. A bona fide measure of quantum entanglement is introduced, the $\mathcal{C}^{t}_q$ -concurrence ( $q \geq 2$ ), which is based on the total concurrence. Analytical lower bounds for the $\mathcal{C}^{t}_q$ -concurrence are derived. In addition, an analytical expression is derived for the $\mathcal{C}^{t}_q$ -concurrence in the cases of isotropic and Werner states. Furthermore, the monogamy relations that the $\mathcal{C}^{t}_q$ -concurrence satisfies for qubit systems are examined. Additionally, based on the parameterized $α$ -concurrence and its complementary dual, the $\mathcal{C}^{t}_α$ -concurrence $(0\leqα\leq\frac{1}{2})$ is also proposed.Quantum entanglement is a crucial resource in quantum information processing, advancing quantum technologies. The greater the uncertainty in subsystems' pure states, the stronger the quantum entanglement between them. From the dual form of $q$-concurrence ($q\geq 2$) we introduce the total concurrence. A bona fide measure of quantum entanglement is introduced, the $\mathcal{C}^{t}_q$-concurrence ($q \geq 2$), which is based on the total concurrence. Analytical lower bounds for the $\mathcal{C}^{t}_q$-concurrence are derived. In addition, an analytical expression is derived for the $\mathcal{C}^{t}_q$-concurrence in the cases of isotropic and Werner states. Furthermore, the monogamy relations that the $\mathcal{C}^{t}_q$-concurrence satisfies for qubit systems are examined. Additionally, based on the parameterized $α$-concurrence and its complementary dual, the $\mathcal{C}^{t}_α$-concurrence $(0\leqα\leq\frac{1}{2})$ is also proposed.

quant-pharXiv:2512.24057Advanced Quantum TechnologiesDec 31, 20254 citations

Classification of Three-Qubit Genuine Entangled States Using Concurrence Fill

Shruti Aggarwal

arXiv:2506.16935International Journal of Theoretical PhysicsOct 16, 20251 citation

Search for an Entanglement Measure for N-Qubit States via Phase Symmetry

Joshua Geller

Bulletin of the American Physical SocietyMar 21, 20110 citations

Parameterized Bipartite Entanglement Measures and Entanglement Constraints

Wen Zhou, Zhong‐Xi Shen, Dong‐Ping Xuan +2 more

Abstract This work proposes a novel class of parameterized entanglement measures that are named as ‐concurrence () (), and demonstrates comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, an analytical formula relating to concurrence for the range of within two‐qubit systems is derived. Additionally, a new polygamy relation of multiqubit quantum entanglement in terms of ‐concurrence of assistance () is proved. However, it fails to obey the monogamy relation, but it is demonstrated that the squared ‐concurrence () does obey a general monogamy relation in an arbitrary ‐qubit mixed state. Utilizing the monogamy properties of , the corresponding multipartite entanglement indicators can be constructed, which can detect all genuine multiqubit entangled states even in the case of ‐tangle vanishes. In addition, for multipartite higher‐dimensional systems, it is illustrated that still has the applicability of the monogamy relation.Abstract This work proposes a novel class of parameterized entanglement measures that are named as ‐concurrence () (), and demonstrates comprehensively that they satisfy all the necessary axiomatic conditions required for an entanglement measure. Furthermore, an analytical formula relating to concurrence for the range of within two‐qubit systems is derived. Additionally, a new polygamy relation of multiqubit quantum entanglement in terms of ‐concurrence of assistance () is proved. However, it fails to obey the monogamy relation, but it is demonstrated that the squared ‐concurrence () does obey a general monogamy relation in an arbitrary ‐qubit mixed state. Utilizing the monogamy properties of , the corresponding multipartite entanglement indicators can be constructed, which can detect all genuine multiqubit entangled states even in the case of ‐tangle vanishes. In addition, for multipartite higher‐dimensional systems, it is illustrated that still has the applicability of the monogamy relation.

arXiv:2503.14245Advanced Quantum TechnologiesMar 17, 20253 citations

Entanglement measure for pure six-qubit quantum states

João Luzeilton de Oliveira, David Sena Oliveira, Rubens Viana Ramos

Quantum Information ProcessingMay 19, 20113 citations

Parameterized genuine multipartite entanglement measure based on

\alpha

-concurrence

q

-concurrence (

q\geq 2

) we introduce the total concurrence. A bona fide measure of quantum entanglement is introduced, the

\mathcal{C}^{t}_q

-concurrence (

q \geq 2

), which is based on the total concurrence. Analytical lower bounds for the

\mathcal{C}^{t}_q

-concurrence are derived. In addition, an analytical expression is derived for the

\mathcal{C}^{t}_q

-concurrence in the cases of isotropic and Werner states. Furthermore, the monogamy relations that the

\mathcal{C}^{t}_q

-concurrence satisfies for qubit systems are examined. Additionally, based on the parameterized

α

-concurrence and its complementary dual, the

\mathcal{C}^{t}_α

-concurrence

(0\leqα\leq\frac{1}{2})

is also proposed.