  Entanglement between degrees of freedom, namely between the spin, path and
(total) energy degrees of freedom, for single neutrons is exploited. We
implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and
coherently manipulated relative phases of two-level quantum subsystems. An
inequality derived by Mermin was applied to analyze the generated GHZ-like
state: we determined the four expectation values and finally obtained M=2.558
+/- 0.004 which is clearly above the threshold of 2. This demonstrates the
violation of a Mermin-like inequality for triply entangled GHZ-like state in a
single-particle system, which, in turn, exhibits a clear inconsistency between
noncontextual assumptions and quantum mechanics and confirms quantum
contextuality.
