Monogamy relations of nonclassical correlations for multi-qubit states

Highlights: • Measurement-induced nonlocality is upper bounded by Bell nonlocaliy. • There exists a strict monogamy relation of MIN for pure three-qubit states. • There is a different monogamy relation of MIN for mixed three-qubit states and even arbitrary n-qubit states. - Abstract: Nonclassical correlations have been found useful in many quantum information processing tasks, and various measures have been proposed to quantify these correlations. In this work, we mainly study one of nonclassical correlations, called measurement-induced nonlocality (MIN). First, we establish a close connection between this nonlocal effect and the Bell nonlocality for two-qubit states. Then, we derive a tight monogamy relation of MIN for any pure three-qubit state and provide an alternative way to obtain similar monogamy relations for other nonclassical correlation measures, including squared negativity, quantum discord, and geometric quantum discord. Finally, we find that the tight monogamy relation of MIN is violated by some mixed three-qubit states, however, a weaker monogamy relation of MIN for mixed states and even multi-qubit states is still obtained.