Quantum steering borders in three-qubit systems

We discuss a family of states describing three-qubit systems in a context of quantum steering phenomena. We show that symmetric steering cannot appear between two qubits—only asymmetric steering can appear in such systems. The main aim of this paper is to discuss the possible relations between the entanglement measures and steering parameter for two-mode mixed state corresponding to the qubit–qubit subsystem. We have derived the conditions determining boundary values of the negativity parametrized by concurrence. We show that two-qubit mixed state cannot be steerable when the negativity of such state is smaller than, or equal to, its boundary value. Finally, we have found ranges of the values of the mixedness measure, parametrized by concurrence and negativity for steerable and unsteerable two-qubit mixed states.