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We investigate the entanglement, CHSH nonlocality, fully entangled fractionand symmetric extendibility of two-qubit states that have a single maximallymixed marginal. Within this set of states, the steering ellipsoid formalism hasrecently highlighted an interesting family of so-called 'maximally obese'states. These are found to have extremal quantum correlation properties thatare significant in the steering ellipsoid picture and for the study oftwo-qubit states in general.

Quantum correlations of two-qubit states with one maximally mixed marginal