  Quantum contextuality, as proved by Kochen and Specker, and also by Bell,
should manifest itself in any state in any system with more than two
distinguishable states and recently has been experimentally verified on various
physical systems. However for the simplest system capable of exhibiting
contextuality, a qutrit, the quantum contextuality is verified only
state-dependently in experiment because too many (at least 31) observables are
involved in all the known state-independent tests. Here we report an
experimentally testable inequality involving only 13 observables that is
satisfied by all non-contextual realistic models while being violated by all
qutrit states. Thus our inequality will practically facilitate a
state-independent test of the quantum contextuality for an indivisible quantum
system. We provide also a record-breaking state-independent proof of the
Kochen-Specker theorem with 13 directions determined by 26 points on the
surface of a three by three magic cube.
