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The norms of Bloch vectors and a trade-off relation of svetlichny inequalities. (English) Zbl 1398.81034

Summary: 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.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
81P16 Quantum state spaces, operational and probabilistic concepts
81P05 General and philosophical questions in quantum theory
90C27 Combinatorial optimization
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
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