Trade-off relations on CHSH tests for multi-qubit pure states

We study the trade-off relations on the maximal violation of CHSH tests for the multi-qubit pure states. Firstly, according to the classification of 3-qubit pure states under stochastic local operations and classical communication, four trade-off relations on CHSH tests are provided. The process of proof also provides the method of calculating its exact value. Then we consider the multi-qubit quantum systems, and we prove that the conjecture in [PRA 94, 042105 (2016)] is right for some special 4-qubit or more qubit pure states.

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