Quantum violation of entropic non-contextual inequality in   four-dimension
  Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of entangled, as well as product states. Our inequality can be experimentally tested using the existing technology. 
A. K. Pan, M. Sumanth, P. K. Panigrahi
quant-ph