The KCBS pentagram inequality is a Bell-type inequality which tests whether given outcomes of measurements performed on Spin-1 systems, are compatible with a description of a joint-probability distribution ("a hidden variable") [1]. Violation of this inequality refutes the existence of such a distribution, testifies that quantum mechanics results cannot be reproduced by any non-contextual hidden variable model (the Kochen-Specker theorem) [2], and thus confirms the context-dependent nature of quantum mechanics.

In this work, we generated photon pairs which represent three-level quantum systems (qutrits), and measured their KCBS value. In order to do so, we used the projection protocol suggested in [1], and adjusted it to the real scenario where some of the biphotons are distinguishable. Our results indicate a KCBS violation by more than four standard deviations, and thus support the contextual description of quantum mechanics. We have also induced noise to the qutrits [3], studied their ability to exhibit the KCBS non-classicality for different levels of the noise, and used the KCBS value as a measure that quantifies the decoherence process that the biphotons have experienced.

[1] A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008).

[2] S. Kochen and E. P. Specker, J. Math. Mech. 17, 59 (1967).

[3] A. Shaham and H. S. Eisenberg, Phys. Rev. A 83, 022303 (2011).