Coherent states and global entanglement in an N qubit system

Abstract

We consider an $N$ qubit system and show that in the symmetric subspace, $\mathbb{S}$ a state is not globally entangled, iff it is a coherent state. It is also proven that in the orthogonal complement $\mathbb{S}_{\bot}$ all states are globally entangled

Exchange symmetry and multipartite entanglement

“…This shows that any state orthogonal to S cannot be fully separable, which is an extension of the previous result [37] for general n.…”

“…Note that the foregoing argument for D is meaningful only if we employ a fixed set of bases in all constituent spaces H i , since otherwise we can always perform unitary transformations in each of the spaces so that any state |ψ ∈ T has the form in (4.11). The characterization of D by (4.11) has been obtained earlier in [37] for n = 2, which is also presented in [38] for generic n in a form equivalent to the latter half of statement (ii) of Theorem 1.…”

Global entanglement and coherent states in an ${\sf N}$ -partite system

“…In a previous paper [11] we considered the question of entanglement of N qubits, while here we present the extension of the problem to the case of "quKits", where the constituent systems are of arbitrary finite dimension, K. We shall prove the statement that a multipartite pure quKit state in the symmetric subspace is not entangled if and only if it is a coherent state, while in the subspace orthogonal to the symmetric one, all states are entangled. A related property between coherent states and entanglement was pointed out earlier in [12] for a two-partite system.…”

Nonlocal correlations for manifold quantum systems: Entanglement of two-spin states

“…Furthermore, they have discussed an other aspects of classicality over the transition in the spin including the distinguishability using the representation of Majorana. Nowadays, studying and understanding structures of quantum entanglement using entangled non-orthogonal states has received much attention; Bosonic entangled coherent states [35][36][37][38] are the typical examples of entangled coherent states. From the point of view of quantum algebra applications to different physical systems, it is important to understand how the behavior of entangled coherent states is modified when the ordinary algebra is modified.…”