N-qubit Entanglement Index and Classification

Details N-qubit Entanglement Index and Classification N-qubit Entanglement Index and Classification

2002-11-21

arxiv.org/abs/quant-ph/0211139v1

Physics

Quantum Physics

2 pages, submitted

Scientific paper

We show that all the N-qubit states can be classified as N entanglement classes each of which has an entanglement index $E=N-p=0,1,...,N-1$(E=0 corresponds to a fully separate class) where $p$ denotes number of groups for a partition of the positive integer N. In other words, for any partition $(n_1,n_2,...,n_p)$ of N with $n_j\ge 1$ and $N=\sum_{j=1}^{p}n_j$, the entanglement index for the corresponding state $\rho_{n_1}\bigotimes\rho_{n_2}...\bigotimes \rho_{n_p}$ with $\rho_{n_j}$ denoting a fully entangled state of $n_j-$qubits is $E(\rho_{n_1}\bigotimes\rho_{n_2}...\bigotimes \rho_{n_p})=\sum_{j=1}^{p}(n_j-1)=N-p$.

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