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理论物理通讯:英文版

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Liu ., Dan Dan, Zhao, Xin, Long, Gui-Lu

Published Jan 1, 2008• 1 citation
OpenAlex

Abstract

Four-qubit 纠纷用一项最近的建议纠纷措施被调查了,多重熵措施(MEMS ) 。我们为 four-qubit 系统的状态的九个不同家庭执行了优化。纠缠的状态被发现了的某 extremal。

Related papers

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

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Communications in Theoretical Physics•Feb 1, 2008•13 citations

Multiple Entropy Measures for Multipartite Quantum Entanglement

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Characterization of four-qubit states via Bell inequalities

Zhao Zhao, Hui Hui, Zhang +4 more

分类 four-qubit 状态的量纠纷的一套贝尔不平等被介绍。这些不平等每观察员包含二个仅仅测量背景并且能描绘充分可分离、双性人可分离、 tri 可分离的量状态。另外,为 four-qubit 系统的贝尔操作符的二次的不平等被导出。

中国科学通报:英文版•Jan 1, 2013•0 citations
A new entanglement measure, the multiple entropy measures (MEMS), is proposed to quantify quantum entanglement of multi-partite quantum state. The MEMS is vector-like with m=[N/2]m=[N/2]m=[N/2], the integer part of N/2N/2N/2, components: [S1,S2,...,Sm][S_1, S_2,..., S_m][S1​,S2​,...,Sm​], and the iii-th component SiS_iSi​ is the geometric mean of iii-body partial entropy of the system. The SiS_iSi​ measures how strong an arbitrary iii bodies from the system are entangled with the rest of the system. The MEMS is not only transparent in physical picture, but also simple to calculate. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states and cluster-states under MEMS. The cluster-state is more entangled than the GHZ-state and W-state under MEMS.
We find an operational interpretation for the 4-tangle as a type of residual entanglement, somewhat similar to the interpretation of the 3-tangle. Using this remarkable interpretation, we are able to find the class of maximally entangled four-qubits states which is characterized by four real parameters. The states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bipartite cuts is maximal. We show that while all the states in the class maximize the average tangle, there are only a few states in the class that maximize the average Tsillas or Renyi α-entropy of entanglement. Quite remarkably, we find that up to local unitaries, there exists two unique states, one maximizing the average α-Tsallis entropy of entanglement for all α ⩾ 2, while the other maximizing it for all 0 < α ⩽ 2 (including the von-Neumann case of α = 1). Furthermore, among the maximally entangled four qubits states, there are only three maximally entangled states that have the property that for two, out of the three bipartite cuts consisting of two-qubits verses two-qubits, the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1 ebit. The unique three maximally entangled states are the three cluster states that are related by a swap operator. We also show that the cluster states are the only states (up to local unitaries) that maximize the average α-Renyi entropy of entanglement for all α ⩾ 2.