Entanglement between degrees of freedom, namely between the spin, path, and (total) energy degrees of freedom, in a single-neutron system is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger (GHZ)–like state and coherently manipulated relative phases of two-level quantum subsystems. An equality derived by Mermin was applied to analyze the generated GHZ-like state: We determined the four expectation values and finally obtained $M=2.558\pm 0.004⩽̸2$. This demonstrates a violation of Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, clearly contradicts the noncontextual assumption and confirms quantum contextuality.

• Received 4 August 2009

DOI:https://doi.org/10.1103/PhysRevA.81.032121