Learn about estimating entanglement monotones in spin systems through this 41-minute seminar presentation from the Quantum Information and Quantum Computing Seminars at CTP PAS. Explore methods for characterizing complex many-body systems by investigating their entanglement structure, focusing on states of N spin-½ particles. Discover approaches for determining and quantifying entanglement using entanglement witnesses and monotones, with emphasis on finding both lower and upper bounds through symmetry-based simplification techniques. Examine thermal states of fully connected spin models described through collective spin observables' first and second moments, with particular attention to permutationally invariant states and optimal spin-squeezing inequalities. Investigate whether these inequalities provide optimal lower bounds to entanglement monotones for spin-squeezed states.