Retrit states violating the KCBS inequality and necessary conditions for maximal contextuality.

Since violations of inequalities implied by non-contextual and local hidden variable theories are observed, it is essential to determine the set of (non-)contextual states. Along this direction, one should determine the conditions under which quantum contextuality is observed. It is also essential to determine how one can find maximally contextual qutrits. In this work, we revisit the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) scenario in which we observe a five-measurement state-dependent contextuality. We investigate possible symmetries of the KCBS pentagram, i.e., the conservation of the contextual characteristic of a qutrit system. For this purpose, the KCBS operator, including five cyclic measurements, is rotated around the Z-axis. We then check a set of rotation angles to determine the contextuality and non-contextuality regions for the eigenstates of the spin-1 operator for an arbitrary rotation. We perform the same operation for the homogeneous linear combination of the eigenstates with spin values +1 and ࢤ1. More generally, we work on the real subgroup of the three-dimensional Hilbert space to determine the set of (non-)contextual states under rotations in the physical Euclidean space 피3. Finally, we show data on Euler rotation angles for which maximally contextual retrits (qutrits of the real Hilbert space) are found and derive mathematical relations through data analysis between Euler angles and qutrit states parameterized with spherical coordinates. We also briefly discuss the general problem of classifying all qutrit states in terms of contextuality. [ABSTRACT FROM AUTHOR]