  We discuss the realization of quantum advantage in a system without quantum
entanglement but with non-zero quantum discord. We propose an optical
realization of symmetric two-qubit $X$-states with controllable anti-diagonal
elements. This approach does not requires initially entangled states, and it
can generate states that have quantum discord, with or without entanglement. We
discuss how quantum advantage can be attained in the context of a two-qubit
game. We show that when entanglement is not present, the maximum quantum
advantage is 1/3 bit. A comparable quantum advantage, 0.311 bit, can be
realized with a simplified transaction protocol involving one vs. the three
unitary operations needed for the maximum advantage.
