Abstract
In the present work we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pair wise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among sub systems. For a three-qubit system, it is impossible that all pairs of qubits violate the steering inequality, and once a pair of qubits violates the steering inequality maximally, the other two pairs of qubits must both obey the steering inequality. We also present a complementarity relation between genuine entanglement present in a tripartite state and maximum bipartite steering violation by its reduced states.
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Roy, A., Bhattacharya, S.S., Mukherjee, A. et al. Several trade off features of quantum steering in distributed scenario. Eur. Phys. J. D 73, 66 (2019). https://doi.org/10.1140/epjd/e2019-90184-3
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DOI: https://doi.org/10.1140/epjd/e2019-90184-3