Abstract
We investigate the norms of Bloch vectors in four-partite quantum systems. An upper bound for the sum of the norms of three-order Bloch vectors has been obtained. We then present a trade-off relation of the Svetlichny inequality for any multipartite qubits systems by the upper bound. We show that for four-qubit systems, the reduced triple qubits cannot reach the maximal violate value simultaneously, while for any six-qubit state, the reduced triple qubits cannot violate Svetlichny inequality in the same time.
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