Multipartite entanglement measure based on multidimensional complementarity

Via a multidimensional complementarity relation we derive an operational entanglement measure for any discrete quantum system, i.e., for any multidimensional and multipartite system. This measure admits a separation into different classes of entanglement obtained by using a flip operator $2,3,\dots{},n$ times, defining a $m$ -flip concurrence. This operator sum has the practical feature to allow one to calculate for mixed states bounds on this $m$ -flip concurrence. Moreover, the information content of an $n$ -partite multidimensional system admits a simple and intuitive interpretation in terms of single particle obtainable information, entanglement, and information due to lack of classical knowledge of the quantum state under investigation. Explicitly, the three qubit system is analyzed and, e.g., the physical difference in entanglement of the W state, the Greenberger-Horne-Zeilinger (GHZ) state, or a biseparable state is revealed.Via a multidimensional complementarity relation we derive an operational entanglement measure for any discrete quantum system, i.e., for any multidimensional and multipartite system. This measure admits a separation into different classes of entanglement obtained by using a flip operator $2,3,\dots{},n$ times, defining a $m$-flip concurrence. This operator sum has the practical feature to allow one to calculate for mixed states bounds on this $m$-flip concurrence. Moreover, the information content of an $n$-partite multidimensional system admits a simple and intuitive interpretation in terms of single particle obtainable information, entanglement, and information due to lack of classical knowledge of the quantum state under investigation. Explicitly, the three qubit system is analyzed and, e.g., the physical difference in entanglement of the W state, the Greenberger-Horne-Zeilinger (GHZ) state, or a biseparable state is revealed.

arXiv:0712.0346Physical Review AJul 22, 200845 citations

Geometric multipartite entanglement measures

Gerardo A. Paz-Silva, John Henry Reina

arXiv:quant-ph/0603102Physics Letters AJan 9, 20074 citations

A multipartite entanglement measure based on coefficient matrices

Chao Zhao, Guowu Yang, William N. N. Hung +1 more

Quantum Information ProcessingMay 15, 201512 citations

Multipartite entanglement in four-qubit cluster-class states

Yan-Kui Bai, Z. D. Wang

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation ${E}_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum state. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation ${E}_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum state. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.

arXiv:0709.4642Physical Review AMar 7, 200845 citations

Bipartite entanglement measures and entanglement constraints

Hui Li, Ting Gao, Fengli Yan

Science China Information SciencesNov 7, 20253 citations

Environment mediated multipartite and multidimensional entanglement

Chee‐Kong Lee, Mojdeh S. Najafabadi, Dániel Schumayer +2 more

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.

arXiv:1902.08320Feb 22, 20191 citation

2,3,\dots{},n

times, defining a

m

-flip concurrence. This operator sum has the practical feature to allow one to calculate for mixed states bounds on this

m

-flip concurrence. Moreover, the information content of an

n

-partite multidimensional system admits a simple and intuitive interpretation in terms of single particle obtainable information, entanglement, and information due to lack of classical knowledge of the quantum state under investigation. Explicitly, the three qubit system is analyzed and, e.g., the physical difference in entanglement of the W state, the Greenberger-Horne-Zeilinger (GHZ) state, or a biseparable state is revealed.

{E}_{ms}

is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum state. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.