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arXiv 1003.4774quant-ph
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偶n量子比特的n-纠缠与剩余纠缠的关系

Relationship between the n-tangle and the residual entanglement of even n qubits

X. Li, D. Li

备注：
8 pages, no figures
发表信息：
Quantum Inf. Comput. 10, 1018 (2010)
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摘要：

我们表明，$n$ -缠结，推广的3-缠结甚至$n$量子比特，是平方的SLOCC多项式不变量的次数为2。我们发现$n$ -缠结不是任何偶数$n\geq 4$ \量子位的剩余纠缠。给出了共生$C_{1(2...n)}$消失的一个充要条件.该条件意味着对任意纠缠态，纠缠度$% C_{1(2...n)}$总是正的，而对某些纠缠态，纠缠度$n$ %为零.我们认为，对于偶数$n$ \量子位，并发度$C_{1(2...n)}$ \等于或大于$n$ % -缠结。进一步，我们揭示了剩余纠缠是任何$n$量子比特的乘积态的部分度量，而$n$ -纠缠对某些乘积态是乘法的.

英文摘要：

We show that $n$-tangle, the generalization of the 3-tangle to even $n$ qubits, is the square of the SLOCC polynomial invariant of degree 2. We find that the $n$-tangle is not the residual entanglement for any even $n\geq 4$\ qubits. We give a necessary and sufficient condition for the vanishing of the concurrence $C_{1(2...n)}$. The condition implies that the concurrence $% C_{1(2...n)}$ is always positive for any entangled states while the $n$% -tangle vanishes for some entangled states. We argue that for even $n$\ qubits, the concurrence $C_{1(2...n)}$\ is equal to or greater than the $n$% -tangle. Further,\ we reveal that the residual entanglement is a partial measure for product states of any $n$ qubits while the $n$-tangle is multiplicative for some product states.

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