For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.

arXiv:1502.01272Physical Review AApr 16, 201536 citations

Tripartite Entanglement in Quantum Open Systems

Habtom Woldekristos

Jan 1, 20091 citation

Detecting genuine multipartite entanglement using moments of positive maps

Saheli Mukherjee, Bivas Mallick, Sahil Gopalkrishna Naik +2 more

Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.

arXiv:2506.00162Physical Review ANov 18, 20256 citations

Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum–one-photon superpositions

Jian Wang, Huan Liu, Xue-feng Zhan +1 more

Utilizing a tritter with variable parameter $T$ and induced by vacuum--one-photon superpositions $|0\ensuremath{\rangle}+\ensuremath{\alpha}|1\ensuremath{\rangle}$ with $\ensuremath{\alpha}=|\ensuremath{\alpha}|{e}^{i\ensuremath{\phi}}$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}={c}_{0}|000\ensuremath{\rangle}+{c}_{1}|100\ensuremath{\rangle}+{c}_{2}|010\ensuremath{\rangle}+{c}_{3}|001\ensuremath{\rangle}$. The coefficients $({c}_{0},$ ${c}_{1},$ ${c}_{2}, \text{and} {c}_{3})$ can be manipulated through interaction parameters $(|\ensuremath{\alpha}|,$ $\ensuremath{\phi}, \text{and} T)$. In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ by using the measure of concurrence fill. Drawing on Hao et al.'s research [Phys. Rev. Lett. 128, 120402 (2022)], we examine tripartite steering for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.Utilizing a tritter with variable parameter $T$ and induced by vacuum--one-photon superpositions $|0\ensuremath{\rangle}+\ensuremath{\alpha}|1\ensuremath{\rangle}$ with $\ensuremath{\alpha}=|\ensuremath{\alpha}|{e}^{i\ensuremath{\phi}}$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}={c}_{0}|000\ensuremath{\rangle}+{c}_{1}|100\ensuremath{\rangle}+{c}_{2}|010\ensuremath{\rangle}+{c}_{3}|001\ensuremath{\rangle}$. The coefficients $({c}_{0},$ ${c}_{1},$ ${c}_{2}, \text{and} {c}_{3})$ can be manipulated through interaction parameters $(|\ensuremath{\alpha}|,$ $\ensuremath{\phi}, \text{and} T)$. In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ by using the measure of concurrence fill. Drawing on Hao et al.'s research [Phys. Rev. Lett. 128, 120402 (2022)], we examine tripartite steering for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.

arXiv:2401.14328Physical Review AAug 26, 20240 citations

Tripartite state characterization via activated bipartite entanglement

L. G. E. Arruda, W. F. Balthazar, Marina V. Moreira +3 more

arXiv:2112.15500Physics Letters AJan 10, 20251 citation

Utilizing a tritter with variable parameter

T

and induced by vacuum--one-photon superpositions $|0\ensuremath{\rangle}+\ensuremath{\alpha}|1\ensuremath{\rangle}$ with $\ensuremath{\alpha}=|\ensuremath{\alpha}|{e}^{i\ensuremath{\phi}}$, we propose a scheme to prepare a class of three-qubit pure states. These states take the form of ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}={c}_{0}|000\ensuremath{\rangle}+{c}_{1}|100\ensuremath{\rangle}+{c}_{2}|010\ensuremath{\rangle}+{c}_{3}|001\ensuremath{\rangle}$. The coefficients

({c}_{0},

{c}_{1},

{c}_{2}, \text{and} {c}_{3})

can be manipulated through interaction parameters $(|\ensuremath{\alpha}|,$ $\ensuremath{\phi}, \text{and} T)$. In line with Xie and Eberly's work [Phys. Rev. Lett. 127, 040403 (2021)], we investigate the genuine tripartite entanglement for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ by using the measure of concurrence fill. Drawing on Hao et al.'s research [Phys. Rev. Lett. 128, 120402 (2022)], we examine tripartite steering for ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ under certain measurements based on the uncertainty relations criterion. We identify nine potential configurations exhibiting varying steerability across different parameter spaces. It is important to highlight that, while the state ${|\ensuremath{\psi}\ensuremath{\rangle}}_{123}$ exhibits entanglement, steering remains unattainable in a substantial portion of the parameter space.