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Abstract
The detection of quantum correlations and the trade-off relationships of correlation resources in multi-partite systems are vitally important in quantum information theory. We present the trade-off relation of any quantum state with respect to the steering inequality and the trade-off relation of generalized Greenberger–Horne–Zeilinger state with respect to the Mermin inequality. We also provide a quantitative analysis of the allocation of associated resources in multi-partite quantum systems. Computable formula of the maximal violation of the Śliwa inequality for any three-qubit state is presented.
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