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 $ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p}$ with $ρ_{n_j}$ denoting a fully entangled state of $n_j-$ qubits is $E(ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p})=\sum_{j=1}^{p}(n_j-1)=N-p$ .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 $ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p}$ with $ρ_{n_j}$ denoting a fully entangled state of $n_j-$qubits is $E(ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p})=\sum_{j=1}^{p}(n_j-1)=N-p$.

arXiv:quant-ph/0211139Nov 21, 20021 citation

Entanglement classification of four-partite states under the SLOCC

S. M. Zangi, Junli Li, Cong‐Feng Qiao

Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.

arXiv:1701.04155Journal of Physics A Mathematical and TheoreticalJun 19, 201719 citations

Entanglement classification of symmetric N-qubit States

Thierry Bastin, Stéphanie Krins, Pierre Mathonet +3 more

Jan 1, 20090 citations

Operational Entanglement Classification for Symmetric N-Qubit States

Thierry Bastin

Jan 1, 20090 citations

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

ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p}

with

ρ_{n_j}

denoting a fully entangled state of

n_j-

qubits is

E(ρ_{n_1}\bigotimesρ_{n_2}...\bigotimes ρ_{n_p})=\sum_{j=1}^{p}(n_j-1)=N-p