We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.

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-1/2s have modelled 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 $\{|j = 1,\mu\langle; \mu = + 1, 0, -12\}$. Our technique relies on the decomposition of a Hamiltonian in terms of $SU$(3) basis matrices. 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.

One of the main problems of quantum information theory is developing the separability criterion which is both necessary and sufficient in nature. Positive partial transposition test (PPT) is one such criterion which is both necessary and sufficient for $2 \times 2$ and $2 \times 3$ systems but not otherwise. We express this strong PPT criterion for a system of 2-qubit symmetric states in terms of the well-known Fano statistical tensor parameters and prove that a large set of separable symmetric states are characterised by real statistical tensor parameters only. The physical importance of these states are brought out by employing trivariate representation of density matrix wherein the components of J, namely $J_{x} , J_{y} , J_{z}$ are considered to be the three variates.We prove that this set of separable states is characterised by the vanishing average expectation value of $J_{y}$ and its covariance with $J_{x}$ and $J_{z}$ . This allows us to identify a symmetric separable state easily. We illustrate our criterion using 2-qubit system as an example.