Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is $2/N.$ This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state $|0〉$ and the others in the basis state $|1〉.$ Quantum entanglement cannot be unlimitedly shared among an arbitrary number of qubits. The degree of bipartite entanglement decreases as the number of entangled pairs in an N-qubit system increases. We analyze a system of N qubits in which an arbitrary pair of particles is entangled. We show that the maximum degree of entanglement (measured in the concurrence) between any pair of qubits is $2/N.$ This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state $|0〉$ and the others in the basis state $|1〉.$

arXiv:quant-ph/0007086Physical Review AOct 16, 2000143 citations

Entanglement classification of symmetric N-qubit States

Thierry Bastin, Stéphanie Krins, Pierre Mathonet +3 more

Jan 1, 20090 citations

Operational entanglement families of symmetric mixed N -qubit states

Thierry Bastin, Pierre Mathonet, E. Solano

We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC entanglement classes successively embedded into each other, we prove that they are of nonzero measure, and we construct witness operators to distinguish them. Moreover, we discuss how arbitrary symmetric mixed states can be realized in the laboratory via a one-to-one correspondence between well-defined sets of controllable parameters and the corresponding entanglement families.We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC entanglement classes successively embedded into each other, we prove that they are of nonzero measure, and we construct witness operators to distinguish them. Moreover, we discuss how arbitrary symmetric mixed states can be realized in the laboratory via a one-to-one correspondence between well-defined sets of controllable parameters and the corresponding entanglement families.

arXiv:1011.1243Physical Review AFeb 12, 201519 citations

QUANTUM ENTANGLEMENT AND SYMMETRIES

Marek Kuś

International Symposium on Quantum Theory and Symmetries (QTS)Jun 1, 20020 citations

Genuinely entangled symmetric states with no N -partite correlations

Sébastien Designolle, O. Giraud, John Martin

We investigate genuinely entangled $N$ -qubit states with no $N$ -partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$ -partite correlations. We show that symmetric states with no $N$ -partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$ -partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd number of qubits.We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd number of qubits.

arXiv:1707.04103Physical Review ASep 12, 20177 citations

Pairwise entanglement in symmetric multi-qubit systems

X. Wang, Klaus Mølmer

arXiv:quant-ph/0106145The European Physical Journal DMar 1, 200264 citations

2/N.

This tight bound can be achieved when the qubits are prepared in a pure symmetric (with respect to permutations) state with just one qubit in the basis state

|0〉

and the others in the basis state

|1〉.

We investigate genuinely entangled

N

-qubit states with no

N

-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of

N

-partite correlations. We show that symmetric states with no

N

-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no

N

-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd number of qubits.