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arXiv 2510.04449quant-ph
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每个量子比特的简化的密度矩阵的平均行列式作为全局纠缠度量

The average determinant of the reduced density matrices for each qubit as a global entanglement measure

Tsinghua University(清华大学)

Dafa Li

AI总结:

本文提出基于量子比特简化的密度矩阵平均行列式的全局纠缠度量,证明其与平均混合度和1-纠缠度的关系,并针对不同量子比特数目的态进行验证。

摘要:

在本文中,我们提出每个量子比特的简化的密度矩阵的平均行列式作为全局纠缠度量。通过简化的密度矩阵的性质,我们可以研究该度量。我们提出该度量的分解定律,证明该度量仅测量每个量子比特的平均混合度和平均1-纠缠度,并指出对于n个量子比特的W态和Dicke态,当量子比特数量较大时,每个量子比特的平均混合度和1-纠缠度几乎消失。我们还指出,对于两个量子比特,该度量只是纠缠度的平方,而对于三个量子比特,该度量是3-纠缠度与两倍平均2-纠缠度之和。

英文摘要:

In this paper, we propose the average determinant of reduced density matrices for each qubit as a global entanglement measure. By means of the properties of reduced density matrices, we can investigate the present measure. We propose a decomposition law for the present measure, demonstrate that the present measure just measures the average mixedness for each qubit and the average 1-tangle, and indicate that for n-qubit W state and Dicke states, the average mixedness for each qubit and 1-tangle almost vanish for the large number of qubits. We also point out that for two qubits, the present measure is just the square of the concurrence while for three qubits, the present measure is the sum of the 3-tangle and the twice the average 2-tangle.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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