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We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein---Podolsky---Rosen steering ellipsoids corresponding to these states.

SLOCC orbit of rank-deficient two-qubit states: quantum entanglement, quantum discord and EPR steering