A method for systematic construction of Bell-like inequalities and a proposal of a new type of test

摘要

The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, which is proven inthe context of the local hidden variable theory, has been used as a test toreveal failure of the hidden variable theory and to prove validity of thequantum theory. We note that violation of the BCHSH inequality is caused bynoncommutativity of quantum observables and find a systematic method forconstructing generalizations of the BCHSH inequality. This method is appliedfor inventing a new quantity which is defined in a two-qubit system andsatisfies a new type of inequality. This provides a fair test of the quantumtheory. Remaining problems are also discussed.