The CHSH Test is Sufficient to Observe the KCBS-Type Quantum Contextuality

Abstract

In this work, we show that the well-known Bell test called Clauser-Horne-Shimony-Holt (CHSH) does not only exhibit non-locality but also the KCBS-type contextuality. For this purpose, we investigate the symmetric subgroup of two-qubit states corresponding to qutrit states (three-level quantum states), which exhibit the KCBS-type (non-)contextuality. Later, we apply the CHSH test to them and find a new non-contextuality bound for this test. This shows us that the CHSH inequality can be modified by changing the limit to use it as a KCBS-type contextuality test. Also, the number of measurements required is four, less than the number of measurements in the KCBS test (That is five).