Monogamy relations for quantum steering of multi-qubit states

Quantum steering plays a fundamental role in quantum information processing regime. In particular, there are two steering-related concepts: one is the quantum steering ellipsoid, which has been used to visualize the two-qubit state, and the other is the Einstein-Podolsky-Rosen (EPR) steering that is a nonlocal correlation between entanglement and Bell nonlocality. In this work, we study the monogamy phenomenon for these two steering properties of the general n-qubit states with n > 4. First, we conjecture that there is a universal tradeoff relation in terms of the spin correlation matrices of reduced bipartite states. From this relation, we can derive the similar monogamy relation for the volume of quantum steering ellipsoids and the linear EPR-steering witness.