Local Invariants and Pairwise Entanglement in Symmetric Multiqubit System

Abstract

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.

Spin squeezing in Dicke-class of states with non-orthogonal spinors

“…Spin squeezing has been an intense area of study due to its theoretical importance as well as the applicability of spin squeezed states in the fields of low noise, high precision spectroscopy [27][28][29] and quantum information science. [10,11,[13][14][15][16] The relative ease with which spin squeezed states can be produced, [10,26] has made them more accessible and hence useful in the concerned fields.…”

“…[31,32] Recently, permutation symmetric states have received a revived attention in diverse branches of physics due to their geometrical intuition and experimental importance. [13,14,33,34] Dicke states |s, m , the common eigenstates of Ŝ2 , Ŝz belonging respectively to eigenvalues s(s + 1)h 2 , mh, m = −s, −s + 1, . .…”

“…An analysis of spin squeezing in the Dicke-class of states with two distinct non-orthogonal spinors, taking into account all possible degeneracy configurations among them, is the aim of this work. In view of the connection between spin squeezing and pairwise entanglement in multiqubit states, [11,[13][14][15][16] this study will be quite useful in quantum information science.…”

Quantum entanglement in multiparticle systems of two-level atoms

“…[5] and [6], regarding the presence of quantum entanglement in a quantum system, forms an important step toward the understanding of quantum entanglement in the context of bipartite states. It has also been found that spin squeezing has a close relationship with quantum entanglement and a lot of work has been done in this direction [7][8][9][10][11][12][13]. A system that is in a spin squeezed state is also quantum mechanically entangled.…”