Discrete phase-space description of N-partite quantum systems: from visualization to quantification of quantum correlations

We review the application of the discrete phase-space approach to analyzing quantum correlations in many body systems. Starting with a microscopic description, we proceed to analyze global features of quantum states detectable in collective measurements, mainly focusing on N-qubit systems in the macroscopic limit N>>1. Applications to quantification/identification of quantum correlations, quantum tomography, phase transitions, quantum thermalization, and stability under local noise are outlined. A generalization to higher local dimensions is discussed.