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We show how mapping techniques inherent to $N^{2}$-dimensional discrete phasespaces can be used to treat a wide family of spin systems which exhibitssqueezing and entanglement effects. This algebraic framework is then applied tothe modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the timeevolution of certain special parameters related to theRobertson-Schr\"{o}dinger (RS) uncertainty principle and some particularproposals of entanglement measure based on collective angular-momentumgenerators. Our results reinforce the connection between both the squeezing andentanglement effects, as well as allow to investigate the basic role of spincorrelations through the discrete representatives of quasiprobabilitydistribution functions. Entropy functionals are also discussed in this context.The main sequence correlations -> entanglement -> squeezing of quantum effectsembraces a new set of insights and interpretations in this framework, whichrepresents an effective gain for future researches in different spin systems.

Spin squeezing and entanglement via finite-dimensional discrete phase-space description