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Steerability is a characteristic nonlocal trait of quantum states lying inbetween entanglement and Bell nonlocality. A given quantum state is consideredto be steerable if it violates a suitably chosen steering inequality. A quantumstate which otherwise satisfies a certain inequality can violate the inequalityunder a global change of basis i.e, if the state is transformed by a nonlocalunitary operation. Intriguingly there are states which preserve theirnon-violation(pertaining to the said inequality) under any global unitaryoperation. The present work explores the effect of global unitary operations onthe steering ability of a quantum state which live in two qubits. Wecharacterize such states in terms of a necessary and sufficient condition ontheir spectrum. Such states are also characterized in terms of some analyticcharacteristics of the set to which they belong. Looking back at steerabilitythe present work also provides a relation between steerability and quantumteleportation together with the derivation of a result related to the optimalviolation of steering inequality . An analytic estimation of the size of suchnon-violating states in terms of purity is also obtained. Interestingly theestimation in terms of purity also gives a necessary and sufficient conditionin terms of bloch parameters of the state. Illustrations from some signatureclass of quantum states further underscore our observations.

Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States