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Abstract. The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors. §

Abstract. The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector S below a certain limit. This aspect has been studied earlier [1,2] for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin-spin correlations.

In this paper, we shall establish the connection between the group theory and quantum mechanics by showing how the group theory helps us to construct the spin operators. We look to the group generators SU(3).

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.