Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.

Co-variance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-j state can be visualized as being made up of 2j spinors which are represented by a constellation of 2j points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.

Abstract. Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2's have modeled a wide range of problems in physics. Here we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, µ ; µ = +1, 0, −1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) generators. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators J x ,J y ,J z . We construct and study the properties of perfect entanglers acting on a symmetric subspace i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.

We study three qubit symmetric states by employing a new representation for the corresponding density matrix. Symmetric N-qubit state is equivalent to well known angular momentum state, | jm where { j = N/2, m = + j to− j } which is also known as Dicke state. The fifteen parameters which characterize the density matrix are real and provide physical interpretation as they are related to first, second and third order moments of spin operators J x , J y , J z . Non-zero parameters for some well known entangled states are obtained.